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University of Illinois – Urbana-Champaign

1. Li, Chunyi. Deformations of the Hilbert scheme of points on a del Pezzo surface.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/49684

► The Hilbert scheme of n points in a smooth del Pezzo surface S parameterizes zero-dimensional subschemes with length n on S. We construct a flat…
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Subjects/Keywords: Hilbert scheme; deformation theory; del Pezzo surface

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

APA (6^{th} Edition):

Li, C. (2014). Deformations of the Hilbert scheme of points on a del Pezzo surface. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49684

Chicago Manual of Style (16^{th} Edition):

Li, Chunyi. “Deformations of the Hilbert scheme of points on a del Pezzo surface.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/49684.

MLA Handbook (7^{th} Edition):

Li, Chunyi. “Deformations of the Hilbert scheme of points on a del Pezzo surface.” 2014. Web. 10 Jul 2020.

Vancouver:

Li C. Deformations of the Hilbert scheme of points on a del Pezzo surface. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/49684.

Council of Science Editors:

Li C. Deformations of the Hilbert scheme of points on a del Pezzo surface. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49684

University of Illinois – Urbana-Champaign

2. Kydonakis, Georgios A. Gluing constructions for Higgs bundles over a complex connected sum.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/100920

► For a compact Riemann surface of genus g ≥ 2, the components of the moduli space of {Sp(4}{,}ℝ{)}-Higgs bundles, or equivalently the {Sp(4}{,}ℝ{)}-character variety, are partially…
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Subjects/Keywords: Higgs bundles; character variety; topological invariants

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

APA (6^{th} Edition):

Kydonakis, G. A. (2018). Gluing constructions for Higgs bundles over a complex connected sum. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/100920

Chicago Manual of Style (16^{th} Edition):

Kydonakis, Georgios A. “Gluing constructions for Higgs bundles over a complex connected sum.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/100920.

MLA Handbook (7^{th} Edition):

Kydonakis, Georgios A. “Gluing constructions for Higgs bundles over a complex connected sum.” 2018. Web. 10 Jul 2020.

Vancouver:

Kydonakis GA. Gluing constructions for Higgs bundles over a complex connected sum. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/100920.

Council of Science Editors:

Kydonakis GA. Gluing constructions for Higgs bundles over a complex connected sum. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/100920

3. Liu, Chih-Chung. The analytic and asymptotic behaviors of vortices.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/44328

► We study vortex equations with a parameter s on smooth vector bundles E over compact Kähler manifolds M. For each s, we invoke techniques in…
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Subjects/Keywords: Vortex Equations; Mathematical Physics; L^2 Geometry; Differential Geometry.

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

APA (6^{th} Edition):

Liu, C. (2013). The analytic and asymptotic behaviors of vortices. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/44328

Chicago Manual of Style (16^{th} Edition):

Liu, Chih-Chung. “The analytic and asymptotic behaviors of vortices.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/44328.

MLA Handbook (7^{th} Edition):

Liu, Chih-Chung. “The analytic and asymptotic behaviors of vortices.” 2013. Web. 10 Jul 2020.

Vancouver:

Liu C. The analytic and asymptotic behaviors of vortices. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/44328.

Council of Science Editors:

Liu C. The analytic and asymptotic behaviors of vortices. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/44328

4. To, Jin Hyung. Holomorphic chains on the projective line.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/31129

► Holomorphic chains on a smooth algebraic curve are tuples of vector bundles on the curve together with the homomorphisms between them. A type of a…
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Subjects/Keywords: Holomorphic chains; α-stability; Chamber; Geometric Invariant Theory (GIT); Nonreductive GIT; Symplectic quotient; Co-Higgs bundles.

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

APA (6^{th} Edition):

To, J. H. (2012). Holomorphic chains on the projective line. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/31129

Chicago Manual of Style (16^{th} Edition):

To, Jin Hyung. “Holomorphic chains on the projective line.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/31129.

MLA Handbook (7^{th} Edition):

To, Jin Hyung. “Holomorphic chains on the projective line.” 2012. Web. 10 Jul 2020.

Vancouver:

To JH. Holomorphic chains on the projective line. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/31129.

Council of Science Editors:

To JH. Holomorphic chains on the projective line. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/31129

5. Gao, Xinghua. Orderability of homology spheres obtained by Dehn filling.

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

URL: http://hdl.handle.net/2142/105627

► In my thesis, I study left-orderability of ℚ-homology spheres. I use \widetilde{PSL_{2}ℝ} representations as a tool. First, I showed this tool has its limitations by…
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Subjects/Keywords: left-orderable group; $\widetilde{PSL_2\mathbb{R}}$ representation

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

APA (6^{th} Edition):

Gao, X. (2019). Orderability of homology spheres obtained by Dehn filling. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/105627

Chicago Manual of Style (16^{th} Edition):

Gao, Xinghua. “Orderability of homology spheres obtained by Dehn filling.” 2019. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/105627.

MLA Handbook (7^{th} Edition):

Gao, Xinghua. “Orderability of homology spheres obtained by Dehn filling.” 2019. Web. 10 Jul 2020.

Vancouver:

Gao X. Orderability of homology spheres obtained by Dehn filling. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2019. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/105627.

Council of Science Editors:

Gao X. Orderability of homology spheres obtained by Dehn filling. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2019. Available from: http://hdl.handle.net/2142/105627

6. Tsai, Chia-Yen. Minimal pseudo-Anosov translation lengths on the Teichmuller space.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16103

► This thesis is a study of the asymptotic behavior of minimal pseudo-Anosov translation lengths on the Teichmuller space. For tori with n marked points, we…
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Subjects/Keywords: pseudo-Anosov; dilatation; mapping class group; Teichmuller space

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

APA (6^{th} Edition):

Tsai, C. (2010). Minimal pseudo-Anosov translation lengths on the Teichmuller space. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16103

Chicago Manual of Style (16^{th} Edition):

Tsai, Chia-Yen. “Minimal pseudo-Anosov translation lengths on the Teichmuller space.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/16103.

MLA Handbook (7^{th} Edition):

Tsai, Chia-Yen. “Minimal pseudo-Anosov translation lengths on the Teichmuller space.” 2010. Web. 10 Jul 2020.

Vancouver:

Tsai C. Minimal pseudo-Anosov translation lengths on the Teichmuller space. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/16103.

Council of Science Editors:

Tsai C. Minimal pseudo-Anosov translation lengths on the Teichmuller space. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16103

7. Fu, Yong. Quantum cohomology of a Hilbert scheme of a Hirzebruch surface.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16874

► In this thesis, we first use the {ℂ^*}^{2}-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some…
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Subjects/Keywords: Gromov-Witten invariants; quantum product

Record Details Similar Records

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

APA (6^{th} Edition):

Fu, Y. (2010). Quantum cohomology of a Hilbert scheme of a Hirzebruch surface. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16874

Chicago Manual of Style (16^{th} Edition):

Fu, Yong. “Quantum cohomology of a Hilbert scheme of a Hirzebruch surface.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/16874.

MLA Handbook (7^{th} Edition):

Fu, Yong. “Quantum cohomology of a Hilbert scheme of a Hirzebruch surface.” 2010. Web. 10 Jul 2020.

Vancouver:

Fu Y. Quantum cohomology of a Hilbert scheme of a Hirzebruch surface. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/16874.

Council of Science Editors:

Fu Y. Quantum cohomology of a Hilbert scheme of a Hirzebruch surface. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16874

8. Sheshmani, Artan. Towards studying of the higher rank theory of stable pairs.

Degree: PhD, 0439, 2011, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/26229

► This thesis is composed of two parts. In the first part we introduce a higher rank analog of the Pandharipande-Thomas theory of stable pairs on…
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Subjects/Keywords: Calabi-Yau threefold; Stable pairs; Deformation-obstruction theory; Derived categories; Equivariant cohomology; Virtual localization; Wallcrossing

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

APA (6^{th} Edition):

Sheshmani, A. (2011). Towards studying of the higher rank theory of stable pairs. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/26229

Chicago Manual of Style (16^{th} Edition):

Sheshmani, Artan. “Towards studying of the higher rank theory of stable pairs.” 2011. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/26229.

MLA Handbook (7^{th} Edition):

Sheshmani, Artan. “Towards studying of the higher rank theory of stable pairs.” 2011. Web. 10 Jul 2020.

Vancouver:

Sheshmani A. Towards studying of the higher rank theory of stable pairs. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/26229.

Council of Science Editors:

Sheshmani A. Towards studying of the higher rank theory of stable pairs. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2011. Available from: http://hdl.handle.net/2142/26229