On duality of certain GKZ hypergeometric systems
Lev Borisov, Zengrui Han, Chengxi Wang
TL;DR
This paper investigates duality properties of specific GKZ hypergeometric systems related to mirror symmetry and confirms conjectures in two-dimensional cases, advancing understanding of their mathematical structure.
Contribution
It proves conjectures on duality of GKZ hypergeometric systems for two-dimensional cases, linking them to mirror symmetry and toric geometry.
Findings
Conjectures on duality are verified in 2D cases.
Establishes connections between GKZ systems and mirror symmetry.
Provides mathematical proof for specific hypergeometric systems.
Abstract
We study a pair of conjectures on better behaved GKZ hypergeometric systems of PDEs inspired by Homological mirror symmetry for crepant resolutions of Gorenstein toric singularities. We prove the conjectures in the case of dimension two.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications