Hodge-theoretic mirror symmetry for toric stacks
File(s)
Accepted version
Author(s)
Coates, T
Corti, A
Iritani, H
Tseng, H-H
Type
Journal Article
Abstract
Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror
description for the big equivariant quantum cohomology of toric Deligne-Mumford
stacks. More precisely, we prove that the big equivariant quantum D-module of a
toric Deligne-Mumford stack is isomorphic to the Saito structure associated to
the mirror Landau-Ginzburg potential. We give a GKZ-style presentation of the
quantum D-module, and a combinatorial description of quantum cohomology as a
quantum Stanley-Reisner ring. We establish the convergence of the mirror
isomorphism and of quantum cohomology in the big and equivariant setting.
description for the big equivariant quantum cohomology of toric Deligne-Mumford
stacks. More precisely, we prove that the big equivariant quantum D-module of a
toric Deligne-Mumford stack is isomorphic to the Saito structure associated to
the mirror Landau-Ginzburg potential. We give a GKZ-style presentation of the
quantum D-module, and a combinatorial description of quantum cohomology as a
quantum Stanley-Reisner ring. We establish the convergence of the mirror
isomorphism and of quantum cohomology in the big and equivariant setting.
Date Issued
2020-05-01
Date Acceptance
2017-07-27
Citation
Journal of Differential Geometry, 2020, 114 (1), pp.41-115
ISSN
1945-743X
Publisher
International Press
Start Page
41
End Page
115
Journal / Book Title
Journal of Differential Geometry
Volume
114
Issue
1
Copyright Statement
©2020 International Press
Sponsor
The Royal Society
Commission of the European Communities
The Royal Society
Identifier
http://arxiv.org/abs/1606.07254v1
Grant Number
UF090056
240123
516002.K5822/kk
Subjects
math.AG
math.AG
math.SG
Notes
58 pages, 3 figures
Publication Status
Published
Date Publish Online
2019-12-28