Hodge-theoretic mirror symmetry for toric stacks

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Title: Hodge-theoretic mirror symmetry for toric stacks
Authors: Coates, T
Corti, A
Iritani, H
Tseng, H-H
Item 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.
Date of Acceptance: 27-Jul-2017
URI: http://hdl.handle.net/10044/1/50273
ISSN: 1945-743X
Publisher: International Press
Journal / Book Title: Journal of Differential Geometry
Copyright Statement: This article is under embargo until publication
Sponsor/Funder: The Royal Society
Commission of the European Communities
The Royal Society
Funder's Grant Number: 516002.K5822/kk
240123
UF090056
Keywords: math.AG
math.AG
math.SG
math.AG
math.AG
math.SG
0101 Pure Mathematics
General Mathematics
Notes: 58 pages, 3 figures
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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