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1. Lozano Huerta, Cesar A. Birational Geometry of the Space of Complete Quadrics.

Degree: 2014, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/18779

Let X be the moduli space of complete (n-1)-quadrics. In this thesis, we study the birational geometry of X using tools from the minimal model program (MMP).
In Chapter 1, we recall the definition of the space X and summarize our main results in Theorems A, B and C.
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In Chapter 2, we examine the codimension-one cycles of the space X, and exhibit generators for Eff(X) and Nef(X) (Theorem A), the cone of effective divisors and the cone of nef divisors, respectively. This result, in particular, allows us to conclude the space X is a Mori dream space.
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In Chapter 3, we study the following question: when does a model of X, defined as X(D):= {Proj}(\bigoplus_{m ≥ 0}H^{0}(X,mD)), have a moduli interpretation? We describe such an interpretation for the models X(H_{k}) (Theorem B), where H_{k} is any generator of the nef cone {Nef}(X). In the case of complete quadric surfaces there are 11 birational models X(D) (Theorem B), where D is a divisor in the movable cone {Mov}(X), and among which we find a moduli interpretation for seven of them.
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Chapter 4 outlines the relation of this work with that of Semple , as well as future directions of research.
*Advisors/Committee Members: Coskun, Izzet (advisor), Ein, Lawrence (committee member), Popa, Mihnea (committee member), Huizenga, Jack (committee member), De Fernex, Tommaso (committee member).*

Subjects/Keywords: algebraic gemeotry; birational geometry; complete quadrics; minimal model program; Mori's program; Hassett-Keel program; moduli spaces

…no reason for this to be the case. However, *Hassett* and *Keel*
first exhibited this… …found by *Hassett* and *Keel*,
holds true for the models of the moduli space of complete quadric… …we study the
birational geometry of X using tools from the minimal model *program* (MMP… …*Program* (MMP). Specifically, we want to understand the birational geometry of the… …notion of Mori dream space was introduced by *Keel* and Hu in (8) and it gives
name to…

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

APA (6^{th} Edition):

Lozano Huerta, C. A. (2014). Birational Geometry of the Space of Complete Quadrics. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/18779

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):

Lozano Huerta, Cesar A. “Birational Geometry of the Space of Complete Quadrics.” 2014. Thesis, University of Illinois – Chicago. Accessed July 12, 2020. http://hdl.handle.net/10027/18779.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Lozano Huerta, Cesar A. “Birational Geometry of the Space of Complete Quadrics.” 2014. Web. 12 Jul 2020.

Vancouver:

Lozano Huerta CA. Birational Geometry of the Space of Complete Quadrics. [Internet] [Thesis]. University of Illinois – Chicago; 2014. [cited 2020 Jul 12]. Available from: http://hdl.handle.net/10027/18779.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lozano Huerta CA. Birational Geometry of the Space of Complete Quadrics. [Thesis]. University of Illinois – Chicago; 2014. Available from: http://hdl.handle.net/10027/18779

Not specified: Masters Thesis or Doctoral Dissertation

2. Mayanskiy, Evgeny S. An asymptotic Mukai model of M6.

Degree: PhD, Mathematics, 2013, Penn State University

URL: https://etda.libraries.psu.edu/catalog/18733

We study the Mukai construction of a general curve of
genus 6 as a complete intersection of the Grassmannian of lines in
P4 with a codimension 5 quadric in the Pl{ücker space. We
formulate the relevant GIT problem in general and then solve it for
the large values of the GIT parameter. This allows us to conclude
that asymptotically Mukai compact model of M6 parametrizes double
anticanonical curves on the smooth del Pezzo surface of degree 5.
As a byproduct of our study we obtain an explicit geometric
interpretation of Ozeki classification of orbits of a certain
prehomogeneous space. This complements earlier results of J.A. Todd
[17].

Subjects/Keywords: Genus 6 curves; Mukai models; Hassett-Keel program; geometric invariant theory

Record Details Similar Records

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

APA (6^{th} Edition):

Mayanskiy, E. S. (2013). An asymptotic Mukai model of M6. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/18733

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

Mayanskiy, Evgeny S. “An asymptotic Mukai model of M6.” 2013. Doctoral Dissertation, Penn State University. Accessed July 12, 2020. https://etda.libraries.psu.edu/catalog/18733.

MLA Handbook (7^{th} Edition):

Mayanskiy, Evgeny S. “An asymptotic Mukai model of M6.” 2013. Web. 12 Jul 2020.

Vancouver:

Mayanskiy ES. An asymptotic Mukai model of M6. [Internet] [Doctoral dissertation]. Penn State University; 2013. [cited 2020 Jul 12]. Available from: https://etda.libraries.psu.edu/catalog/18733.

Council of Science Editors:

Mayanskiy ES. An asymptotic Mukai model of M6. [Doctoral Dissertation]. Penn State University; 2013. Available from: https://etda.libraries.psu.edu/catalog/18733