Toric mirror symmetry and GIT windows

"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."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Huang, Jesse

Contributors dc:contributor

• Pascaleff, James
• Katz, Sheldon
• Tolman, Susan
• Dodd, Christopher

• toric variety
• mirror symmetry
• window subcategory

Statement dc:rights

• Copyright 2021 Jesse Huang

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/113112