subject:(Algebraic Geometry)

University of Illinois – Urbana-Champaign

1. Hong, Euijin. Two problems in the theory of curves over fields of positive characteristic.

Degree: PhD, Mathematics, 2019, University of Illinois – Urbana-Champaign

► This thesis consists of two parts. In the first half, we define, so called, generalized Artin-Schreier cover of a scheme X over k. After defining… (more)

Subjects/Keywords: Algebraic Geometry; Algebraic Geometry Code

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APA (6^th Edition):

Hong, E. (2019). Two problems in the theory of curves over fields of positive characteristic. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/104786

Chicago Manual of Style (16^th Edition):

Hong, Euijin. “Two problems in the theory of curves over fields of positive characteristic.” 2019. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed December 15, 2019. http://hdl.handle.net/2142/104786.

MLA Handbook (7^th Edition):

Hong, Euijin. “Two problems in the theory of curves over fields of positive characteristic.” 2019. Web. 15 Dec 2019.

Vancouver:

Hong E. Two problems in the theory of curves over fields of positive characteristic. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2019. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/2142/104786.

Council of Science Editors:

Hong E. Two problems in the theory of curves over fields of positive characteristic. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2019. Available from: http://hdl.handle.net/2142/104786

Kansas State University

2. Abou-Rached, John. Sheaves and schemes: an introduction to algebraic geometry.

Degree: MS, Department of Mathematics, 2016, Kansas State University

URL: http://hdl.handle.net/2097/32608

► The purpose of this report is to serve as an introduction to the language of sheaves and schemes via algebraic geometry. The main objective is… (more)

Subjects/Keywords: Algebraic Geometry

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APA (6^th Edition):

Abou-Rached, J. (2016). Sheaves and schemes: an introduction to algebraic geometry. (Masters Thesis). Kansas State University. Retrieved from http://hdl.handle.net/2097/32608

Chicago Manual of Style (16^th Edition):

Abou-Rached, John. “Sheaves and schemes: an introduction to algebraic geometry.” 2016. Masters Thesis, Kansas State University. Accessed December 15, 2019. http://hdl.handle.net/2097/32608.

MLA Handbook (7^th Edition):

Abou-Rached, John. “Sheaves and schemes: an introduction to algebraic geometry.” 2016. Web. 15 Dec 2019.

Vancouver:

Abou-Rached J. Sheaves and schemes: an introduction to algebraic geometry. [Internet] [Masters thesis]. Kansas State University; 2016. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/2097/32608.

Council of Science Editors:

Abou-Rached J. Sheaves and schemes: an introduction to algebraic geometry. [Masters Thesis]. Kansas State University; 2016. Available from: http://hdl.handle.net/2097/32608

3. Lai, Kuan-Wen. Cremona transformations and rational parametrizations inspired by Hodge theory.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792697/

► This thesis exhibits two of the author's works: the first is about interpreting the derived equivalences of K3 surfaces through Cremona transformations, where we construct… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Lai, K. (2018). Cremona transformations and rational parametrizations inspired by Hodge theory. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792697/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lai, Kuan-Wen. “Cremona transformations and rational parametrizations inspired by Hodge theory.” 2018. Thesis, Brown University. Accessed December 15, 2019. https://repository.library.brown.edu/studio/item/bdr:792697/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lai, Kuan-Wen. “Cremona transformations and rational parametrizations inspired by Hodge theory.” 2018. Web. 15 Dec 2019.

Vancouver:

Lai K. Cremona transformations and rational parametrizations inspired by Hodge theory. [Internet] [Thesis]. Brown University; 2018. [cited 2019 Dec 15]. Available from: https://repository.library.brown.edu/studio/item/bdr:792697/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lai K. Cremona transformations and rational parametrizations inspired by Hodge theory. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792697/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

4. Marcus, Steffen S. Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes.

Degree: PhD, Mathematics, 2011, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11253/

► The main subject of this dissertation is the study of certain moduli spaces intimately related to the enumerative geometry of complex algebraic varieties and orbifolds.… (more)

▼ The main subject of this dissertation is the study of certain moduli spaces intimately related to the enumerative geometry of complex algebraic varieties and orbifolds. In three separate but related directions, we contribute to the development and use of recent variants of Gromov-Witten (GW) theory and relative GW theory. The work of this dissertation took place in collaborative projects with Dan Abramovich, Renzo Cavalieri, Qile Chen, William Gillam, Henning Ulfarsson and Jonathan Wise.Very twisted stable maps.We construct the moduli stack of very twisted stable maps to a smooth projective Deligne-Mumford stack, extending the notion of twisted stable maps (due to Abramovich and Vistoli) to allow for generic stabilizers on the source curves. We also consider the GW theory given by this construction.The evaluation space of logarithmic stable maps.The evaluation stack for minimal logarithmic stable maps is constructed, parameterizing families of standard log points in the target log scheme. This construction provides the ingredients necessary to define appropriate evaluation maps for minimal log stable maps and establish the logarithmic GW theory of a log-smooth Deligne-Faltings log scheme.Polynomial families of tautological classes on the moduli space of curves.We study double Hurwitz classes on the rational tails locus of the moduli space of curves. These are defined by pushing forward the virtual fundamental classes of spaces of relative stable maps to an unparameterized projective line with prescribed ramification over zero and infinity. A comparison with classes arising from sections of the universal Jacobian shows that double Hurwitz classes are polynomial in the parts of the partitions indexing the special ramification data. Virtual localization on moduli spaces of relative stable maps gives sufficient relations to compute the coefficients of these polynomials in various cases. Advisors/Committee Members: Abramovich, Dan (Director), Cavalieri, Renzo (Reader), Lichtenbaum, Stephen (Reader).

Subjects/Keywords: algebraic geometry

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APA (6^th Edition):

Marcus, S. S. (2011). Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11253/

Chicago Manual of Style (16^th Edition):

Marcus, Steffen S. “Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes.” 2011. Doctoral Dissertation, Brown University. Accessed December 15, 2019. https://repository.library.brown.edu/studio/item/bdr:11253/.

MLA Handbook (7^th Edition):

Marcus, Steffen S. “Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes.” 2011. Web. 15 Dec 2019.

Vancouver:

Marcus SS. Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes. [Internet] [Doctoral dissertation]. Brown University; 2011. [cited 2019 Dec 15]. Available from: https://repository.library.brown.edu/studio/item/bdr:11253/.

Council of Science Editors:

Marcus SS. Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes. [Doctoral Dissertation]. Brown University; 2011. Available from: https://repository.library.brown.edu/studio/item/bdr:11253/

5. Ascher, Kenneth Brian. Higher Dimensional Birational Geometry: Moduli and Arithmetic.

Degree: Department of Mathematics, 2017, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:733261/

► While the study of algebraic curves and their moduli has been a celebrated subject in algebraic and arithmetic geometry, generalizations of many results that hold… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Ascher, K. B. (2017). Higher Dimensional Birational Geometry: Moduli and Arithmetic. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:733261/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ascher, Kenneth Brian. “Higher Dimensional Birational Geometry: Moduli and Arithmetic.” 2017. Thesis, Brown University. Accessed December 15, 2019. https://repository.library.brown.edu/studio/item/bdr:733261/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ascher, Kenneth Brian. “Higher Dimensional Birational Geometry: Moduli and Arithmetic.” 2017. Web. 15 Dec 2019.

Vancouver:

Ascher KB. Higher Dimensional Birational Geometry: Moduli and Arithmetic. [Internet] [Thesis]. Brown University; 2017. [cited 2019 Dec 15]. Available from: https://repository.library.brown.edu/studio/item/bdr:733261/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ascher KB. Higher Dimensional Birational Geometry: Moduli and Arithmetic. [Thesis]. Brown University; 2017. Available from: https://repository.library.brown.edu/studio/item/bdr:733261/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Pennsylvania

6. Deliu, Dragos. Homological Projective Duality for Gr(3,6).

Degree: 2011, University of Pennsylvania

URL: https://repository.upenn.edu/edissertations/316

► Homological Projective Duality is a homological extension of the classical no- tion of projective duality. Constructing the homological projective dual of a variety allows one… (more)

Subjects/Keywords: Algebraic Geometry

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APA (6^th Edition):

Deliu, D. (2011). Homological Projective Duality for Gr(3,6). (Thesis). University of Pennsylvania. Retrieved from https://repository.upenn.edu/edissertations/316

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Deliu, Dragos. “Homological Projective Duality for Gr(3,6).” 2011. Thesis, University of Pennsylvania. Accessed December 15, 2019. https://repository.upenn.edu/edissertations/316.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Deliu, Dragos. “Homological Projective Duality for Gr(3,6).” 2011. Web. 15 Dec 2019.

Vancouver:

Deliu D. Homological Projective Duality for Gr(3,6). [Internet] [Thesis]. University of Pennsylvania; 2011. [cited 2019 Dec 15]. Available from: https://repository.upenn.edu/edissertations/316.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Deliu D. Homological Projective Duality for Gr(3,6). [Thesis]. University of Pennsylvania; 2011. Available from: https://repository.upenn.edu/edissertations/316

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

7. Bejleri, Dori. A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792818/

► Moduli spaces play a central role in algebraic geometry. In this thesis we study the geometry of two particular moduli spaces. In Part I we… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Bejleri, D. (2018). A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792818/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bejleri, Dori. “A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces.” 2018. Thesis, Brown University. Accessed December 15, 2019. https://repository.library.brown.edu/studio/item/bdr:792818/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bejleri, Dori. “A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces.” 2018. Web. 15 Dec 2019.

Vancouver:

Bejleri D. A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces. [Internet] [Thesis]. Brown University; 2018. [cited 2019 Dec 15]. Available from: https://repository.library.brown.edu/studio/item/bdr:792818/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bejleri D. A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792818/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

8. Harper, Alicia Deen. Factorization of Deligne-Mumford Stacks.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792829/

► We prove a weak factorization result on birational maps of Deligne-Mumford stacks, and deduce the following: Let U \subset X be an open embedding of… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Harper, A. D. (2018). Factorization of Deligne-Mumford Stacks. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792829/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Harper, Alicia Deen. “Factorization of Deligne-Mumford Stacks.” 2018. Thesis, Brown University. Accessed December 15, 2019. https://repository.library.brown.edu/studio/item/bdr:792829/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Harper, Alicia Deen. “Factorization of Deligne-Mumford Stacks.” 2018. Web. 15 Dec 2019.

Vancouver:

Harper AD. Factorization of Deligne-Mumford Stacks. [Internet] [Thesis]. Brown University; 2018. [cited 2019 Dec 15]. Available from: https://repository.library.brown.edu/studio/item/bdr:792829/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Harper AD. Factorization of Deligne-Mumford Stacks. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792829/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

9. Molcho, Samouil. Logarithmic Stable Maps with Torus Actions.

Degree: PhD, Mathematics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386232/

► We study the moduli stacks of logarithmic stable maps when the target variety X is equipped with an action of a one-dimensional torus C*. Specifically,… (more)

Subjects/Keywords: Algebraic Geometry

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APA (6^th Edition):

Molcho, S. (2014). Logarithmic Stable Maps with Torus Actions. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386232/

Chicago Manual of Style (16^th Edition):

Molcho, Samouil. “Logarithmic Stable Maps with Torus Actions.” 2014. Doctoral Dissertation, Brown University. Accessed December 15, 2019. https://repository.library.brown.edu/studio/item/bdr:386232/.

MLA Handbook (7^th Edition):

Molcho, Samouil. “Logarithmic Stable Maps with Torus Actions.” 2014. Web. 15 Dec 2019.

Vancouver:

Molcho S. Logarithmic Stable Maps with Torus Actions. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2019 Dec 15]. Available from: https://repository.library.brown.edu/studio/item/bdr:386232/.

Council of Science Editors:

Molcho S. Logarithmic Stable Maps with Torus Actions. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386232/

University of Oxford

10. Jackson, Joshua James. Moduli spaces of unstable curves and sheaves via non-reductive geometric invariant theory.

Degree: PhD, 2018, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:d566c8db-433c-4eb5-8611-7f16e2724500 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.772567

► Many moduli problems in algebraic geometry can be posed using Geometric Invariant Theory (GIT). However, as with all such tools, if we are to have… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Jackson, J. J. (2018). Moduli spaces of unstable curves and sheaves via non-reductive geometric invariant theory. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:d566c8db-433c-4eb5-8611-7f16e2724500 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.772567

Chicago Manual of Style (16^th Edition):

Jackson, Joshua James. “Moduli spaces of unstable curves and sheaves via non-reductive geometric invariant theory.” 2018. Doctoral Dissertation, University of Oxford. Accessed December 15, 2019. http://ora.ox.ac.uk/objects/uuid:d566c8db-433c-4eb5-8611-7f16e2724500 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.772567.

MLA Handbook (7^th Edition):

Jackson, Joshua James. “Moduli spaces of unstable curves and sheaves via non-reductive geometric invariant theory.” 2018. Web. 15 Dec 2019.

Vancouver:

Jackson JJ. Moduli spaces of unstable curves and sheaves via non-reductive geometric invariant theory. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2019 Dec 15]. Available from: http://ora.ox.ac.uk/objects/uuid:d566c8db-433c-4eb5-8611-7f16e2724500 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.772567.

Council of Science Editors:

Jackson JJ. Moduli spaces of unstable curves and sheaves via non-reductive geometric invariant theory. [Doctoral Dissertation]. University of Oxford; 2018. Available from: http://ora.ox.ac.uk/objects/uuid:d566c8db-433c-4eb5-8611-7f16e2724500 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.772567

Cornell University

11. Snider, Michelle. Affine Patches On Positroid Varieties And Affine Pipe Dreams .

Degree: 2011, Cornell University

URL: http://hdl.handle.net/1813/33472

► The objects of interest in this thesis are positroid varieties in the Grassmannian, which are indexed by juggling patterns. In particular, we study affine patches… (more)

Subjects/Keywords: algebraic combinatorics; algebraic geometry

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APA (6^th Edition):

Snider, M. (2011). Affine Patches On Positroid Varieties And Affine Pipe Dreams . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/33472

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Snider, Michelle. “Affine Patches On Positroid Varieties And Affine Pipe Dreams .” 2011. Thesis, Cornell University. Accessed December 15, 2019. http://hdl.handle.net/1813/33472.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Snider, Michelle. “Affine Patches On Positroid Varieties And Affine Pipe Dreams .” 2011. Web. 15 Dec 2019.

Vancouver:

Snider M. Affine Patches On Positroid Varieties And Affine Pipe Dreams . [Internet] [Thesis]. Cornell University; 2011. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/1813/33472.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Snider M. Affine Patches On Positroid Varieties And Affine Pipe Dreams . [Thesis]. Cornell University; 2011. Available from: http://hdl.handle.net/1813/33472

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Waterloo

12. Rollick, Nickolas. Approximation Constants for Closed Subschemes of Projective Varieties.

Degree: 2019, University of Waterloo

URL: http://hdl.handle.net/10012/14764

► Diophantine approximation is a branch of number theory with a long history, going back at least to the work of Dirichlet and Liouville in the… (more)

▼ Diophantine approximation is a branch of number theory with a long history, going back at least to the work of Dirichlet and Liouville in the 1840s. The innocent-looking question of how well an arbitrary real algebraic number can be approximated by rational numbers (relative to the size of the denominator of the approximating rational number) took more than 100 years to resolve, culminating in the definitive Fields Medal-winning work of Klaus Roth in 1955. Much more recently, David McKinnon and Mike Roth have re-phrased and generalized this Diophantine approximation question to apply in the setting of approximating algebraic points on projective varieties defined over number fields. To do this, they defined an "approximation constant", depending on the point one wishes to approximate and a given line bundle. This constant measures the tradeoff between the closeness of the approximation and the arithmetic complexity of the point used to make the approximation, as measured by a height function associated to the line bundle. In particular, McKinnon and Roth succeeded in proving lower bounds on the approximation constant in terms of the "Seshadri constant" associated to the given point and line bundle, measuring local positivity of the line bundle around the point. Appropriately interpreted, these results generalize the classical work of Liouville and Roth, and the corresponding McKinnon-Roth theorems are therefore labelled "Liouville-type" and "Roth-type" results. Recent work of Grieve and of Ru-Wang have taken the Roth-type theorems even further; in contrast, we explore results of Liouville-type, which are more elementary in nature. In Chapter 2, we lay the groundwork necessary to define the approximation constant at a point, before generalizing the McKinnon-Roth definition to approximations of arbitrary closed subschemes. We also introduce the notion of an essential approximation constant, which ignores unusually good approximations along proper Zariski-closed subsets. After verifying that our new approximation constant truly does generalize the constant of McKinnon-Roth, Chapter 3 establishes a fundamental lower bound on the approximation constants of closed subschemes of projective space, depending only on the equations cutting out the subscheme. In Chapter 4, we provide a series of explicit computations of approximation constants, both for subschemes satisfying suitable geometric conditions, and for curves of low degree in projective 3-space. We will encounter difficulties computing the approximation constant exactly for general cubic curves, and we spend some time showing why some of the more evident approaches do not succeed. To conclude the chapter, we take up the question of large gaps between the ordinary and essential approximation constants, by considering approximations to a certain rational point on a diagonal quartic surface. Finally, in Chapter 5, we generalize the Liouville-type results of McKinnon-Roth.

Subjects/Keywords: algebraic geometry; algebraic number theory

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APA (6^th Edition):

Rollick, N. (2019). Approximation Constants for Closed Subschemes of Projective Varieties. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/14764

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Rollick, Nickolas. “Approximation Constants for Closed Subschemes of Projective Varieties.” 2019. Thesis, University of Waterloo. Accessed December 15, 2019. http://hdl.handle.net/10012/14764.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Rollick, Nickolas. “Approximation Constants for Closed Subschemes of Projective Varieties.” 2019. Web. 15 Dec 2019.

Vancouver:

Rollick N. Approximation Constants for Closed Subschemes of Projective Varieties. [Internet] [Thesis]. University of Waterloo; 2019. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/10012/14764.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Rollick N. Approximation Constants for Closed Subschemes of Projective Varieties. [Thesis]. University of Waterloo; 2019. Available from: http://hdl.handle.net/10012/14764

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Rutgers University

13. Lee, King Leung, 1987-. Stability and canonical metrics on projective varieties.

Degree: PhD, Mathematical Sciences, 2018, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/57351/

►

This thesis presents some of my works on projective geometry. The first part of this thesis provides some background based on the joint work with… (more)

Subjects/Keywords: Geometry, Algebraic; Geometry, Projective

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APA (6^th Edition):

Lee, King Leung, 1. (2018). Stability and canonical metrics on projective varieties. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/57351/

Chicago Manual of Style (16^th Edition):

Lee, King Leung, 1987-. “Stability and canonical metrics on projective varieties.” 2018. Doctoral Dissertation, Rutgers University. Accessed December 15, 2019. https://rucore.libraries.rutgers.edu/rutgers-lib/57351/.

MLA Handbook (7^th Edition):

Lee, King Leung, 1987-. “Stability and canonical metrics on projective varieties.” 2018. Web. 15 Dec 2019.

Vancouver:

Lee, King Leung 1. Stability and canonical metrics on projective varieties. [Internet] [Doctoral dissertation]. Rutgers University; 2018. [cited 2019 Dec 15]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/57351/.

Council of Science Editors:

Lee, King Leung 1. Stability and canonical metrics on projective varieties. [Doctoral Dissertation]. Rutgers University; 2018. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/57351/

University of Pennsylvania

14. Dyckerhoff, Tobias. Isolated Hypersurface Singularities as Noncommutative Spaces.

Degree: 2010, University of Pennsylvania

URL: https://repository.upenn.edu/edissertations/111

► We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. This category is shown to admit a compact generator… (more)

Subjects/Keywords: Algebra; Algebraic Geometry

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APA (6^th Edition):

Dyckerhoff, T. (2010). Isolated Hypersurface Singularities as Noncommutative Spaces. (Thesis). University of Pennsylvania. Retrieved from https://repository.upenn.edu/edissertations/111

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Dyckerhoff, Tobias. “Isolated Hypersurface Singularities as Noncommutative Spaces.” 2010. Thesis, University of Pennsylvania. Accessed December 15, 2019. https://repository.upenn.edu/edissertations/111.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Dyckerhoff, Tobias. “Isolated Hypersurface Singularities as Noncommutative Spaces.” 2010. Web. 15 Dec 2019.

Vancouver:

Dyckerhoff T. Isolated Hypersurface Singularities as Noncommutative Spaces. [Internet] [Thesis]. University of Pennsylvania; 2010. [cited 2019 Dec 15]. Available from: https://repository.upenn.edu/edissertations/111.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Dyckerhoff T. Isolated Hypersurface Singularities as Noncommutative Spaces. [Thesis]. University of Pennsylvania; 2010. Available from: https://repository.upenn.edu/edissertations/111

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Nevada – Las Vegas

15. Rowe, Nathan P. Structures on a K3 surface.

Degree: MSin Mathematical Science, Mathematical Sciences, 2010, University of Nevada – Las Vegas

URL: https://digitalscholarship.unlv.edu/thesesdissertations/737

► In the first part of this paper, we examine properties of K3 surfaces of the form: (x2 + 1)(y2 + 1)(z2 + 1) +… (more)

Subjects/Keywords: Algebraic Geometry; Mathematics

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APA (6^th Edition):

Rowe, N. P. (2010). Structures on a K3 surface. (Masters Thesis). University of Nevada – Las Vegas. Retrieved from https://digitalscholarship.unlv.edu/thesesdissertations/737

Chicago Manual of Style (16^th Edition):

Rowe, Nathan P. “Structures on a K3 surface.” 2010. Masters Thesis, University of Nevada – Las Vegas. Accessed December 15, 2019. https://digitalscholarship.unlv.edu/thesesdissertations/737.

MLA Handbook (7^th Edition):

Rowe, Nathan P. “Structures on a K3 surface.” 2010. Web. 15 Dec 2019.

Vancouver:

Rowe NP. Structures on a K3 surface. [Internet] [Masters thesis]. University of Nevada – Las Vegas; 2010. [cited 2019 Dec 15]. Available from: https://digitalscholarship.unlv.edu/thesesdissertations/737.

Council of Science Editors:

Rowe NP. Structures on a K3 surface. [Masters Thesis]. University of Nevada – Las Vegas; 2010. Available from: https://digitalscholarship.unlv.edu/thesesdissertations/737

Queens University

16. Smirnov, Ilia. Smooth Complete Intersections with Positive-Definite Intersection Form .

Degree: Mathematics and Statistics, 2012, Queens University

URL: http://hdl.handle.net/1974/7602

► We classify the smooth complete intersections with positive-definite intersection form on their middle cohomology. There are two families. The first family are quadric hypersurfaces in… (more)

Subjects/Keywords: Algebraic Geometry; Mathematics

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APA (6^th Edition):

Smirnov, I. (2012). Smooth Complete Intersections with Positive-Definite Intersection Form . (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/7602

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Smirnov, Ilia. “Smooth Complete Intersections with Positive-Definite Intersection Form .” 2012. Thesis, Queens University. Accessed December 15, 2019. http://hdl.handle.net/1974/7602.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Smirnov, Ilia. “Smooth Complete Intersections with Positive-Definite Intersection Form .” 2012. Web. 15 Dec 2019.

Vancouver:

Smirnov I. Smooth Complete Intersections with Positive-Definite Intersection Form . [Internet] [Thesis]. Queens University; 2012. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/1974/7602.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Smirnov I. Smooth Complete Intersections with Positive-Definite Intersection Form . [Thesis]. Queens University; 2012. Available from: http://hdl.handle.net/1974/7602

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

17. Hazzazi, Mohammad Mazyad M. On decompositions of finite projective planes and their applications.

Degree: PhD, 2019, University of Sussex

URL: http://sro.sussex.ac.uk/id/eprint/83855/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.781742

► Let PG(2; q) be the projective plane over the field Fq. Singer [19] notes that PG(2; q) has a cyclic group of order q2 +… (more)

Subjects/Keywords: QA0564 Algebraic geometry

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APA (6^th Edition):

Hazzazi, M. M. M. (2019). On decompositions of finite projective planes and their applications. (Doctoral Dissertation). University of Sussex. Retrieved from http://sro.sussex.ac.uk/id/eprint/83855/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.781742

Chicago Manual of Style (16^th Edition):

Hazzazi, Mohammad Mazyad M. “On decompositions of finite projective planes and their applications.” 2019. Doctoral Dissertation, University of Sussex. Accessed December 15, 2019. http://sro.sussex.ac.uk/id/eprint/83855/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.781742.

MLA Handbook (7^th Edition):

Hazzazi, Mohammad Mazyad M. “On decompositions of finite projective planes and their applications.” 2019. Web. 15 Dec 2019.

Vancouver:

Hazzazi MMM. On decompositions of finite projective planes and their applications. [Internet] [Doctoral dissertation]. University of Sussex; 2019. [cited 2019 Dec 15]. Available from: http://sro.sussex.ac.uk/id/eprint/83855/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.781742.

Council of Science Editors:

Hazzazi MMM. On decompositions of finite projective planes and their applications. [Doctoral Dissertation]. University of Sussex; 2019. Available from: http://sro.sussex.ac.uk/id/eprint/83855/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.781742

Duke University

18. Diaz, Humberto Antonio. Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles .

Degree: 2016, Duke University

URL: http://hdl.handle.net/10161/12201

► This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines… (more)

Subjects/Keywords: Mathematics; Algebraic Geometry

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APA (6^th Edition):

Diaz, H. A. (2016). Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles . (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/12201

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Diaz, Humberto Antonio. “Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles .” 2016. Thesis, Duke University. Accessed December 15, 2019. http://hdl.handle.net/10161/12201.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Diaz, Humberto Antonio. “Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles .” 2016. Web. 15 Dec 2019.

Vancouver:

Diaz HA. Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles . [Internet] [Thesis]. Duke University; 2016. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/10161/12201.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Diaz HA. Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles . [Thesis]. Duke University; 2016. Available from: http://hdl.handle.net/10161/12201

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Colorado State University

19. Hanson, Eric M. Algorithms in Numerical Algebraic Geometry and Applications.

Degree: PhD, Mathematics, 2015, Colorado State University

URL: http://hdl.handle.net/10217/167182

► The topics in this dissertation, while independent, are unified under the field of numerical algebraic geometry. With ties to some of the oldest areas in… (more)

▼ The topics in this dissertation, while independent, are unified under the field of numerical algebraic geometry. With ties to some of the oldest areas in mathematics, numerical algebraic geometry is relatively young as a field of study in its own right. The field is concerned with the numerical approximation of the solution sets of systems of polynomial equations and the manipulation of these sets. Given a polynomial system ƒ : CN → Cn, the methods of numerical algebraic geometry produce numerical approximations of the isolated solutions of ƒ(z) = 0, as well as points on any positive-dimensional components of the solution set, V(ƒ). In a short time, the work done in numerical algebraic geometry has significantly pushed the boundary of what is computable. This dissertation aims to further this work by contributing new algorithms to the field and using cutting edge techniques of the field to expand the scope of problems that can be addressed using numerical methods. We begin with an introduction to numerical algebraic geometry and subsequent chapters address independent topics: perturbed homotopies, exceptional sets and fiber products, and a numerical approach to finding unit distance embeddings of finite simple graphs. One of the most recent advances in numerical algebraic geometry is regeneration, an equation-by-equation homotopy method that is often more efficient than other approaches. However, the basic form of regeneration will not necessarily find all isolated singular solutions of a polynomial system without the additional cost of using deflation. In the second chapter, we present an alternative to deflation in the form of perturbed homotopies for solving polynomial systems. In particular, we propose first solving a perturbed version of the polynomial system, followed by a parameter homotopy to remove the perturbation. The aim of this chapter is two-fold. First, such perturbed homotopies are sometimes more efficient than regular homotopies, though they can also be less efficient. Second, a useful consequence is that the application of this perturbation to regeneration will yield all isolated solutions, including all singular isolated solutions. The third chapter considers families of polynomial systems which depend on parameters. There is a typical dimension for the variety defined by a system in the family; however, this dimension may jump for parameters in algebraic subsets of the parameter space. Sommese and Wampler exploited fiber products to give a numerical method for identifying these special parameter values. In this chapter, we propose a refined numerical approach to fiber products, which uses recent advancements in numerical algebraic geometry, such as regeneration extension. We show that this method is sometimes more efficient then known techniques. This gain in efficiency is due to the fact that regeneration extension allows the construction of the fiber product to be restricted to specified irreducible components. This work is motivated by applications in Kinematics - the… Advisors/Committee Members: Bates, Daniel J. (advisor), Peterson, Chris (committee member), Cavalieri, Renzo (committee member), Maciejewski, Anthony (committee member).

Subjects/Keywords: Numerical Algebraic Geometry

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APA (6^th Edition):

Hanson, E. M. (2015). Algorithms in Numerical Algebraic Geometry and Applications. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/167182

Chicago Manual of Style (16^th Edition):

Hanson, Eric M. “Algorithms in Numerical Algebraic Geometry and Applications.” 2015. Doctoral Dissertation, Colorado State University. Accessed December 15, 2019. http://hdl.handle.net/10217/167182.

MLA Handbook (7^th Edition):

Hanson, Eric M. “Algorithms in Numerical Algebraic Geometry and Applications.” 2015. Web. 15 Dec 2019.

Vancouver:

Hanson EM. Algorithms in Numerical Algebraic Geometry and Applications. [Internet] [Doctoral dissertation]. Colorado State University; 2015. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/10217/167182.

Council of Science Editors:

Hanson EM. Algorithms in Numerical Algebraic Geometry and Applications. [Doctoral Dissertation]. Colorado State University; 2015. Available from: http://hdl.handle.net/10217/167182

University of Waterloo

20. Castañeda Santos, Diana Carolina. Rational approximations on smooth rational surfaces.

Degree: 2019, University of Waterloo

URL: http://hdl.handle.net/10012/14859

► In this thesis, we study a conjecture made by D. McKinnon about rational approximations to rational points in algebraic varieties. The conjecture states that if… (more)

▼ In this thesis, we study a conjecture made by D. McKinnon about rational approximations to rational points in algebraic varieties. The conjecture states that if a rational point P on a variety X lies on a rational curve, then the best approximations to P can be chosen to lie along a rational curve on X. According to the conditions of the conjecture, it is natural to study this problem on algebraic varieties that contain a dense subset of rational points. Motivated by this remark, we study the conjecture on smooth rational surfaces, which not only contain a dense set of rational points, but also their classification is well understood. Given a point P on an algebraic variety and an ample divisor D, the approximation constant measures how well P can be approximated by rational points on the variety, with respect to a height function associated to D. In the study of the conjecture, it became clear that if a curve C contains the best approximations to P with respect to ample divisors D and D', then C turns out to be also a curve containing the best approximations for any divisor that is a linear combination of D and D'. This property motivated the study of the nef cone of the algebraic variety. Every ample divisor belongs to the interior of the nef cone and can be written as a linear combination of the generators of the nef cone. By an exhaustive study of the effective and nef cones on a smooth rational surface, it is possible to find a curve that contains the best approximations to the point P with respect to an ample divisor, which can be written in terms of the generators of the nef cone. In this work we use the fact that a smooth rational surface is obtained by a finite number of blow-ups of a Hirzebruch surface or of the projective plane. The Hirzebruch surfaces are equipped with morphisms to the projective line and to cones in some projective space. The study of the fibres of these morphisms provide good candidates of curves with best approximations and we rely on them to prove the conjecture for these cases. We review the conjecture proved by McKinnon in the case of smooth rational surfaces of Picard rank 4. We explore some of the examples in this case to present the techniques using the nef cone of the variety, and then we extend the result for surfaces of bigger Picard ranks. Finally, we extend the result to surfaces obtained by blowing up an arbitrary number of times on smooth points of the reducible fibre of the map to the projective line.

Subjects/Keywords: Diophantine approximations; Algebraic geometry; Birational geometry; Arithmetic geometry; Complex algebraic surfaces

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APA (6^th Edition):

Castañeda Santos, D. C. (2019). Rational approximations on smooth rational surfaces. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/14859

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Castañeda Santos, Diana Carolina. “Rational approximations on smooth rational surfaces.” 2019. Thesis, University of Waterloo. Accessed December 15, 2019. http://hdl.handle.net/10012/14859.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Castañeda Santos, Diana Carolina. “Rational approximations on smooth rational surfaces.” 2019. Web. 15 Dec 2019.

Vancouver:

Castañeda Santos DC. Rational approximations on smooth rational surfaces. [Internet] [Thesis]. University of Waterloo; 2019. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/10012/14859.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Castañeda Santos DC. Rational approximations on smooth rational surfaces. [Thesis]. University of Waterloo; 2019. Available from: http://hdl.handle.net/10012/14859

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Louisiana State University

21. Dribus, Benjamin F. On the infinitesimal theory of Chow groups.

Degree: PhD, Applied Mathematics, 2014, Louisiana State University

URL: etd-04062014-182723 ; https://digitalcommons.lsu.edu/gradschool_dissertations/821

► The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to… (more)

▼ The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure. Except for the case p=1, which yields an algebraic group, the Chow groups remain mysterious. This thesis explores a "linearization" approach to this problem, focusing on the infinitesimal structure of the Chow groups near their identity elements. This method was adumbrated in recent work of Mark Green and Phillip Griffiths. Similar topics have been explored by Bloch, Stienstra, Hesselholt, Van der Kallen, and others. A famous formula of Bloch expresses the Chow groups as Zariski sheaf cohomology groups of algebraic K-theory sheaves on X. Bloch's formula follows from the fact that the coniveau spectral sequence for algebraic K-theory on X induces flasque resolutions of these sheaves. Algebraic cycles and algebraic K-theory are thereby related via the general method of coniveau filtration of a topological space. Hence, "linearization" of the Chow groups is related to "linearization" of algebraic K-theory, which may be described in terms of negative cyclic homology. The proper formal construction arising from this approach is a "machine" involving the coniveau spectral sequences arising from four different generalized cohomology theories on X, which I will call K-theory, augmented K-theory, relative K-theory, and relative negative cyclic homology. The objects of principal interest are certain sheaf cohomology groups defined in terms of these theories. In particular, the pth Chow group is the pth cohomology group of the pth K-theory sheaf. Due to the critical role of coniveau filtration, I refer to this construction as the coniveau machine. The main theorem in this thesis establishes the existence of the coniveau machine for algebraic K-theory on a smooth algebraic variety. This result depends on a large body of prior work of Bloch-Ogus, Thomason, Colliot-Thelene, Hoober, and Kahn, Loday, and most recently, Cortinas, Haesemeyer, and Weibel. An immediate corollary is a new formula expressing generalized tangent groups of Chow groups in terms of negative cyclic homology, which is more tractable than algebraic K-theory.

Subjects/Keywords: algebraic geometry; algebraic cycles; Chow groups

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APA (6^th Edition):

Dribus, B. F. (2014). On the infinitesimal theory of Chow groups. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-04062014-182723 ; https://digitalcommons.lsu.edu/gradschool_dissertations/821

Chicago Manual of Style (16^th Edition):

Dribus, Benjamin F. “On the infinitesimal theory of Chow groups.” 2014. Doctoral Dissertation, Louisiana State University. Accessed December 15, 2019. etd-04062014-182723 ; https://digitalcommons.lsu.edu/gradschool_dissertations/821.

MLA Handbook (7^th Edition):

Dribus, Benjamin F. “On the infinitesimal theory of Chow groups.” 2014. Web. 15 Dec 2019.

Vancouver:

Dribus BF. On the infinitesimal theory of Chow groups. [Internet] [Doctoral dissertation]. Louisiana State University; 2014. [cited 2019 Dec 15]. Available from: etd-04062014-182723 ; https://digitalcommons.lsu.edu/gradschool_dissertations/821.

Council of Science Editors:

Dribus BF. On the infinitesimal theory of Chow groups. [Doctoral Dissertation]. Louisiana State University; 2014. Available from: etd-04062014-182723 ; https://digitalcommons.lsu.edu/gradschool_dissertations/821

University of California – Berkeley

22. Geraschenko, Anton Igorevich. Toric Stacks.

Degree: Mathematics, 2011, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/7sp369k8

► The first purpose of this dissertation is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks… (more)

Subjects/Keywords: Mathematics; algebraic geometry; algebraic stacks; toric varieties

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APA (6^th Edition):

Geraschenko, A. I. (2011). Toric Stacks. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/7sp369k8

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Geraschenko, Anton Igorevich. “Toric Stacks.” 2011. Thesis, University of California – Berkeley. Accessed December 15, 2019. http://www.escholarship.org/uc/item/7sp369k8.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Geraschenko, Anton Igorevich. “Toric Stacks.” 2011. Web. 15 Dec 2019.

Vancouver:

Geraschenko AI. Toric Stacks. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2019 Dec 15]. Available from: http://www.escholarship.org/uc/item/7sp369k8.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Geraschenko AI. Toric Stacks. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/7sp369k8

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

23. Halpern-Leistner, Daniel Scott. Geometric invariant theory and derived categories of coherent sheaves.

Degree: Mathematics, 2013, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/3z0991wj

► Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its… (more)

▼ Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its geometric invariant theory quotient. This generalizes classical descriptions of the category of coherent sheaves on projective space and categorifies several results in the theory of Hamiltonian group actions on projective manifolds.This perspective generalizes and provides new insight into examples of derived equivalences between birational varieties. We provide a criterion under which two different GIT quotients are derived equivalent, and apply it to prove that any two generic GIT quotients of an equivariantly Calabi-Yau projective-over-affine variety by a torus are derived equivalent.We also use these techniques to study autoequivalences of the derived category of coherent sheaves of a variety arising from a variation of GIT quotient. We show that these autoequivalences are generalized spherical twists, and describe how they result from mutations of semiorthogonal decompositions. Beyond the GIT setting, we show that all generalized spherical twist autoequivalences of a dg-category can be obtained from mutation in this manner.Motivated by a prediction from mirror symmetry, we refine the main theorem describing the derived category of a GIT quotient. We produce additional derived autoequivalences of a GIT quotient and propose an interpretation in terms of monodromy of the quantum connection. We generalize this observation by proving a criterion under which a spherical twist autoequivalence factors into a composition of other spherical twists.Finally, our technique for studying the derived category of a GIT quotient relies on a special stratification of the unstable locus in GIT. In the final chapter we establish a new modular description of this stratification using the mapping stack from the quotient of the affine line by the multiplicative group to the quotient stack X/G. This is the first foundational step in extending the methods of GIT beyond global quotient stacks X/G to other stacks arising in algebraic geometry. We describe a method of constructing such stratifications for arbitrary algebraic stacks and show that it reproduces the GIT stratification as well as the classical stratification of the moduli stack of vector bundles on a smooth curve.

Subjects/Keywords: Mathematics; algebraic geometry; algebraic stacks; derived categories

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APA (6^th Edition):

Halpern-Leistner, D. S. (2013). Geometric invariant theory and derived categories of coherent sheaves. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/3z0991wj

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Halpern-Leistner, Daniel Scott. “Geometric invariant theory and derived categories of coherent sheaves.” 2013. Thesis, University of California – Berkeley. Accessed December 15, 2019. http://www.escholarship.org/uc/item/3z0991wj.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Halpern-Leistner, Daniel Scott. “Geometric invariant theory and derived categories of coherent sheaves.” 2013. Web. 15 Dec 2019.

Vancouver:

Halpern-Leistner DS. Geometric invariant theory and derived categories of coherent sheaves. [Internet] [Thesis]. University of California – Berkeley; 2013. [cited 2019 Dec 15]. Available from: http://www.escholarship.org/uc/item/3z0991wj.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Halpern-Leistner DS. Geometric invariant theory and derived categories of coherent sheaves. [Thesis]. University of California – Berkeley; 2013. Available from: http://www.escholarship.org/uc/item/3z0991wj

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Georgia

24. Arcara, Daniele. Moduli spaces of vector bundles on curves.

Degree: PhD, Mathematics, 2003, University of Georgia

URL: http://purl.galileo.usg.edu/uga_etd/arcara_daniele_200305_phd

► In this work, we generalize Bertram’s work on rank two vector bundles on a smooth irreducible projective curve to an irreducible singular curve C with… (more)

Subjects/Keywords: Algebraic Geometry

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APA (6^th Edition):

Arcara, D. (2003). Moduli spaces of vector bundles on curves. (Doctoral Dissertation). University of Georgia. Retrieved from http://purl.galileo.usg.edu/uga_etd/arcara_daniele_200305_phd

Chicago Manual of Style (16^th Edition):

Arcara, Daniele. “Moduli spaces of vector bundles on curves.” 2003. Doctoral Dissertation, University of Georgia. Accessed December 15, 2019. http://purl.galileo.usg.edu/uga_etd/arcara_daniele_200305_phd.

MLA Handbook (7^th Edition):

Arcara, Daniele. “Moduli spaces of vector bundles on curves.” 2003. Web. 15 Dec 2019.

Vancouver:

Arcara D. Moduli spaces of vector bundles on curves. [Internet] [Doctoral dissertation]. University of Georgia; 2003. [cited 2019 Dec 15]. Available from: http://purl.galileo.usg.edu/uga_etd/arcara_daniele_200305_phd.

Council of Science Editors:

Arcara D. Moduli spaces of vector bundles on curves. [Doctoral Dissertation]. University of Georgia; 2003. Available from: http://purl.galileo.usg.edu/uga_etd/arcara_daniele_200305_phd

University of Georgia

25. Donnelly, Stephen Robert. Finding elements of given order in Tate-Shafarevich groups of elliptic curves.

Degree: PhD, Mathematics, 2003, University of Georgia

URL: http://purl.galileo.usg.edu/uga_etd/donnelly_stephen_r_200308_phd

► The Tate-Shafarevich group of an elliptic curve over a number field K measures the obstruction to determing the K-rational points by the standard method, which… (more)

Subjects/Keywords: Algebraic geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Donnelly, S. R. (2003). Finding elements of given order in Tate-Shafarevich groups of elliptic curves. (Doctoral Dissertation). University of Georgia. Retrieved from http://purl.galileo.usg.edu/uga_etd/donnelly_stephen_r_200308_phd

Chicago Manual of Style (16^th Edition):

Donnelly, Stephen Robert. “Finding elements of given order in Tate-Shafarevich groups of elliptic curves.” 2003. Doctoral Dissertation, University of Georgia. Accessed December 15, 2019. http://purl.galileo.usg.edu/uga_etd/donnelly_stephen_r_200308_phd.

MLA Handbook (7^th Edition):

Donnelly, Stephen Robert. “Finding elements of given order in Tate-Shafarevich groups of elliptic curves.” 2003. Web. 15 Dec 2019.

Vancouver:

Donnelly SR. Finding elements of given order in Tate-Shafarevich groups of elliptic curves. [Internet] [Doctoral dissertation]. University of Georgia; 2003. [cited 2019 Dec 15]. Available from: http://purl.galileo.usg.edu/uga_etd/donnelly_stephen_r_200308_phd.

Council of Science Editors:

Donnelly SR. Finding elements of given order in Tate-Shafarevich groups of elliptic curves. [Doctoral Dissertation]. University of Georgia; 2003. Available from: http://purl.galileo.usg.edu/uga_etd/donnelly_stephen_r_200308_phd

University of Georgia

26. Gwena, Tawanda. Degenerations of Prym Varieties and cubic threefolds.

Degree: PhD, Mathematics, 2004, University of Georgia

URL: http://purl.galileo.usg.edu/uga_etd/gwena_tawanda_200408_phd

► We present a surprising connection between degenerations of cubic threefolds and well known regular matroids by making use of intermediate Jacobians of cubic threefolds realized… (more)

Subjects/Keywords: Algebraic Geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gwena, T. (2004). Degenerations of Prym Varieties and cubic threefolds. (Doctoral Dissertation). University of Georgia. Retrieved from http://purl.galileo.usg.edu/uga_etd/gwena_tawanda_200408_phd

Chicago Manual of Style (16^th Edition):

Gwena, Tawanda. “Degenerations of Prym Varieties and cubic threefolds.” 2004. Doctoral Dissertation, University of Georgia. Accessed December 15, 2019. http://purl.galileo.usg.edu/uga_etd/gwena_tawanda_200408_phd.

MLA Handbook (7^th Edition):

Gwena, Tawanda. “Degenerations of Prym Varieties and cubic threefolds.” 2004. Web. 15 Dec 2019.

Vancouver:

Gwena T. Degenerations of Prym Varieties and cubic threefolds. [Internet] [Doctoral dissertation]. University of Georgia; 2004. [cited 2019 Dec 15]. Available from: http://purl.galileo.usg.edu/uga_etd/gwena_tawanda_200408_phd.

Council of Science Editors:

Gwena T. Degenerations of Prym Varieties and cubic threefolds. [Doctoral Dissertation]. University of Georgia; 2004. Available from: http://purl.galileo.usg.edu/uga_etd/gwena_tawanda_200408_phd

University of Plymouth

27. Wuria Muhammad Ameen, Hussein. Invariant algebraic surfaces in three dimensional vector fields.

Degree: PhD, 2016, University of Plymouth

URL: http://hdl.handle.net/10026.1/4417

► This work is devoted to investigating the behaviour of invariant algebraic curves for the two dimensional Lotka-Volterra systems and examining almost a geometrical approach for… (more)

Subjects/Keywords: 516.3; application of algebraic geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wuria Muhammad Ameen, H. (2016). Invariant algebraic surfaces in three dimensional vector fields. (Doctoral Dissertation). University of Plymouth. Retrieved from http://hdl.handle.net/10026.1/4417

Chicago Manual of Style (16^th Edition):

Wuria Muhammad Ameen, Hussein. “Invariant algebraic surfaces in three dimensional vector fields.” 2016. Doctoral Dissertation, University of Plymouth. Accessed December 15, 2019. http://hdl.handle.net/10026.1/4417.

MLA Handbook (7^th Edition):

Wuria Muhammad Ameen, Hussein. “Invariant algebraic surfaces in three dimensional vector fields.” 2016. Web. 15 Dec 2019.

Vancouver:

Wuria Muhammad Ameen H. Invariant algebraic surfaces in three dimensional vector fields. [Internet] [Doctoral dissertation]. University of Plymouth; 2016. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/10026.1/4417.

Council of Science Editors:

Wuria Muhammad Ameen H. Invariant algebraic surfaces in three dimensional vector fields. [Doctoral Dissertation]. University of Plymouth; 2016. Available from: http://hdl.handle.net/10026.1/4417

Penn State University

28. Turner, Jacob Wade. The Invariant Theory and Geometry Pertaining to Tensor Networks and Some Further Applications.

Degree: PhD, Mathematics, 2015, Penn State University

URL: https://etda.libraries.psu.edu/catalog/24878

► The main objects of study in this work are tensor networks. We study applications of these objects to problems in computer science and physics using… (more)

Subjects/Keywords: Representation Theory; Algebraic Geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Turner, J. W. (2015). The Invariant Theory and Geometry Pertaining to Tensor Networks and Some Further Applications. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/24878

Chicago Manual of Style (16^th Edition):

Turner, Jacob Wade. “The Invariant Theory and Geometry Pertaining to Tensor Networks and Some Further Applications.” 2015. Doctoral Dissertation, Penn State University. Accessed December 15, 2019. https://etda.libraries.psu.edu/catalog/24878.

MLA Handbook (7^th Edition):

Turner, Jacob Wade. “The Invariant Theory and Geometry Pertaining to Tensor Networks and Some Further Applications.” 2015. Web. 15 Dec 2019.

Vancouver:

Turner JW. The Invariant Theory and Geometry Pertaining to Tensor Networks and Some Further Applications. [Internet] [Doctoral dissertation]. Penn State University; 2015. [cited 2019 Dec 15]. Available from: https://etda.libraries.psu.edu/catalog/24878.

Council of Science Editors:

Turner JW. The Invariant Theory and Geometry Pertaining to Tensor Networks and Some Further Applications. [Doctoral Dissertation]. Penn State University; 2015. Available from: https://etda.libraries.psu.edu/catalog/24878

University of Oregon

29. Lim, Bronson. Equivariant Derived Categories Associated to a Sum of Potentials.

Degree: 2017, University of Oregon

URL: http://hdl.handle.net/1794/22628

► We construct a semi-orthogonal decomposition for the equivariant derived category of a hypersurface associated to the sum of two potentials. More specifically, if f,g are… (more)

Subjects/Keywords: Algebraic geometry; Derived categories

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lim, B. (2017). Equivariant Derived Categories Associated to a Sum of Potentials. (Thesis). University of Oregon. Retrieved from http://hdl.handle.net/1794/22628

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lim, Bronson. “Equivariant Derived Categories Associated to a Sum of Potentials.” 2017. Thesis, University of Oregon. Accessed December 15, 2019. http://hdl.handle.net/1794/22628.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lim, Bronson. “Equivariant Derived Categories Associated to a Sum of Potentials.” 2017. Web. 15 Dec 2019.

Vancouver:

Lim B. Equivariant Derived Categories Associated to a Sum of Potentials. [Internet] [Thesis]. University of Oregon; 2017. [cited 2019 Dec 15]. Available from: http://hdl.handle.net/1794/22628.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lim B. Equivariant Derived Categories Associated to a Sum of Potentials. [Thesis]. University of Oregon; 2017. Available from: http://hdl.handle.net/1794/22628

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Tennessee – Knoxville

30. Ogle, Jacob Andrew. Counting Reducible Composites of Polynomials.

Degree: 2011, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_graddiss/1110

► This research answers some open questions about the number of reducible translates of a fixed non-constant polynomial over a field. The natural hypothesis to consider… (more)

Subjects/Keywords: redset; translates; Algebraic Geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ogle, J. A. (2011). Counting Reducible Composites of Polynomials. (Doctoral Dissertation). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_graddiss/1110

Chicago Manual of Style (16^th Edition):

Ogle, Jacob Andrew. “Counting Reducible Composites of Polynomials.” 2011. Doctoral Dissertation, University of Tennessee – Knoxville. Accessed December 15, 2019. https://trace.tennessee.edu/utk_graddiss/1110.

MLA Handbook (7^th Edition):

Ogle, Jacob Andrew. “Counting Reducible Composites of Polynomials.” 2011. Web. 15 Dec 2019.

Vancouver:

Ogle JA. Counting Reducible Composites of Polynomials. [Internet] [Doctoral dissertation]. University of Tennessee – Knoxville; 2011. [cited 2019 Dec 15]. Available from: https://trace.tennessee.edu/utk_graddiss/1110.

Council of Science Editors:

Ogle JA. Counting Reducible Composites of Polynomials. [Doctoral Dissertation]. University of Tennessee – Knoxville; 2011. Available from: https://trace.tennessee.edu/utk_graddiss/1110

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