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UBC Theses and Dissertations
Birational models of geometric invariant theory quotients Cheung, Elliot
Abstract
In this thesis, we study the problem of finding birational models of projective G-varieties with tame stabilizers. This is done with linearizations, so that each birational model may be considered as a (modular) compactification of an orbit space (of properly stable points). The main portion of the thesis is a re-working of a result in Kirwan's paper "Partial Desingularisations of Quotients of Nonsingular Varieties and their Betti Numbers", written in a purely algebro-geometric language. As such, the proofs are novel and require the Luna Slice Theorem as their primary tool. Chapter 1 is devoted to preliminary material on Geometric Invariant Theory and the Luna Slice Theorem. In Chapter 2, we present and prove a version of "Kirwan's procedure". This chapter concludes with an outline of some differences between the current thesis and Kirwan's original paper. In Chapter 3, we combine the results from Chapter 2 and a result from a paper by Reichstein and Youssin to provide another type of birational model with tame stabilizers (again, with respect to an original linearization).
Item Metadata
Title |
Birational models of geometric invariant theory quotients
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2017
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Description |
In this thesis, we study the problem of finding birational models of projective G-varieties with tame stabilizers. This is done with linearizations, so that each birational model may be considered as a (modular) compactification of an orbit space (of properly stable points).
The main portion of the thesis is a re-working of a result in Kirwan's paper "Partial Desingularisations of Quotients of Nonsingular Varieties and their Betti Numbers", written in a purely algebro-geometric language. As such, the proofs are novel and require the Luna Slice Theorem as their primary tool.
Chapter 1 is devoted to preliminary material on Geometric Invariant Theory
and the Luna Slice Theorem.
In Chapter 2, we present and prove a version of "Kirwan's procedure". This chapter concludes with an outline of some differences between the current thesis and Kirwan's original paper.
In Chapter 3, we combine the results from Chapter 2 and a result from a paper by Reichstein and Youssin to provide another type of birational model with tame stabilizers (again, with respect to an original linearization).
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Genre | |
Type | |
Language |
eng
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Date Available |
2017-04-20
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0343974
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2017-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International