Quantum D-modules of toric varieties and oscillatory integrals
Hiroshi Iritani
TL;DR
This paper reviews the mirror symmetry relating quantum cohomology D-modules of toric varieties to various integral systems and algebraic structures, highlighting their interconnected roles in mirror symmetry.
Contribution
It provides a comprehensive overview of the connections between quantum D-modules, GKZ systems, and Mellin-Barnes integrals in the context of toric varieties.
Findings
Clarifies the relationship between quantum cohomology D-modules and GKZ systems.
Explores the role of Mellin-Barnes integrals and Gamma structures in mirror symmetry.
Summarizes the algebraic and integral representations relevant to toric mirror symmetry.
Abstract
We review mirror symmetry for the quantum cohomology D-module of a compact weak-Fano toric manifold. We also discuss the relationship to the GKZ system, the Stanley-Reisner ring, the Mellin-Barnes integrals, and the Gamma-integral structure.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models