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Permanent link (DOI): https://doi.org/10.7939/R36H4D443

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Hybrid Model Chambers of Toric Geometric Invariant Theory Quotients Open Access

Descriptions

Other title
Subject/Keyword
GKZ Decomposition
Hybrid Model
GIT Quotient
Secondary Fan
Equivariant Vector Bundle
Vector Bundle
Herbst Criterion
Stacky Vector Bundle
Geometric Invariant Theory
Quasisymmetric
Toric Geometry
Algebraic Geometry
Charge Matrix
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Hanratty, Chantelle
Supervisor and department
Favero, David (Mathematical and Statistical Sciences)
Examining committee member and department
Boucahrd, Vincent (Mathematical and Statistical Sciences)
Lewis, James (Mathematical and Statistical Sciences)
Creutzig, Thomas (Mathematical and Statistical Sciences)
Favero, David (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2017-09-28T14:58:44Z
Graduation date
2017-11:Fall 2017
Degree
Master of Science
Degree level
Master's
Abstract
We give an explicit criterion for when a toric GIT quotient is a stacky vector bundle over a projective base. That is given a charge matrix satisfying a certain property, we construct a projective base such that the semi-stable locus of the original GIT quotient is a G-equivariant vector bundle over the semi-stable locus of this base. We also relax this criterion to classify toric GIT quotients which differ from a stacky vector bundle by a finite map. As an application, we recover the Herbst Criterion established by Guffin and Clarke. In addition, we prove that when the G-action is quasisymmetic, there is a finite toric morphism from a product of projective spaces to the base.
Language
English
DOI
doi:10.7939/R36H4D443
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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