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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
  • Graduation date
    2017-11: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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Favero, David (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Favero, David (Mathematical and Statistical Sciences)
    • Creutzig, Thomas (Mathematical and Statistical Sciences)
    • Lewis, James (Mathematical and Statistical Sciences)
    • Boucahrd, Vincent (Mathematical and Statistical Sciences)