Hybrid Model Chambers of Toric Geometric Invariant Theory Quotients

• Author / Creator

  Hanratty, Chantelle

• 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.

• Subjects / Keywords

  • Quasisymmetric
  • Stacky Vector Bundle
  • Herbst Criterion
  • Algebraic Geometry
  • Hybrid Model
  • GIT Quotient
  • Vector Bundle
  • Charge Matrix
  • Equivariant Vector Bundle
  • Toric Geometry
  • Geometric Invariant Theory
  • GKZ Decomposition
  • Secondary Fan

• Graduation date

  Fall 2017

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R36H4D443

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. 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.