University of Illinois Urbana-Champaign

Toric mirror symmetry and GIT windows

Huang, Jesse

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https://hdl.handle.net/2142/113112

Description

Title
Toric mirror symmetry and GIT windows
Author(s)
Huang, Jesse
Issue Date
2021-06-15
Director of Research (if dissertation) or Advisor (if thesis)
Pascaleff, James
Doctoral Committee Chair(s)
Katz, Sheldon
Committee Member(s)
  • Tolman, Susan
  • Dodd, Christopher
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • toric variety
  • mirror symmetry
  • window subcategory
Abstract
"This thesis, partially based on the author's joint work [HZ20], studies mirror symmetry for toric varieties from the perspective of geometric invariant theory. We translate GIT constructions of toric varieties into skeletal terms and study them in the context of wrapped Fukaya categories and wrapped constructible sheaves. We explain how the mirror image of the Halpern-Leistner-Sam ""magic window"" for quasi-symmetric torus actions computes the category associated to the equivariant semistable skeleton upon stop removal, where the generating cotangent fibers are described by a generic shift of a lattice zonotope in the real character space of the torus. After identifying the ""FI parameter space"" of the B-model GLSM with the GKZ complex parameter space of the skeletal LG A-model, homological mirror symmetry in the quasi-symmetric case becomes two geometric incarnations of the Špenko-Van den Bergh schober over C^k stratified by a complexified periodic hyperplane arrangement whose complement models both parameter spaces. We obtain a universal deformation of skeletons interpolating variation of parameters."
Graduation Semester
2021-08
Type of Resource
Thesis
Permalink
http://hdl.handle.net/2142/113112
Copyright and License Information
Copyright 2021 Jesse Huang

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