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Title:Toric mirror symmetry and GIT windows
Author(s):Huang, Jesse
Director of Research:Pascaleff, James
Doctoral Committee Chair(s):Katz, Sheldon
Doctoral Committee Member(s):Tolman, Susan; Dodd, Christopher
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(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.
Issue Date:2021-06-15
Rights Information:Copyright 2021 Jesse Huang
Date Available in IDEALS:2022-01-12
Date Deposited:2021-08

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