Non-affine Landau-Ginzburg models and intersection cohomology

2012/10/24 by Reichelt, Thomas, Sevenheck, Christian · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.6527

Abstract

We construct Landau-Ginzburg models for numerically effective complete intersections in toric manifolds as partial compactifications of families of Laurent polynomials. We show a mirror statement saying that the quantum D-module of the ambient part of the cohomology of the submanifold is isomorphic to an intersection cohomology D-module defined from this partial compactification and we deduce Hodge properties of these differential systems.

Cited by

• Duality theory of tautological systems
• Unfolding of equivariant F-bundles and application to the mirror symmetry of flag varieties

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• Landau-Ginzburg/Calabi-Yau correspondence for a complete intersection via matrix factorizations
• Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models
• A note on cohomology mirror symmetry of toric manifolds