Asian Journal of Mathematics

Volume 25 (2021)

Number 1

On duality of certain GKZ hypergeometric systems

Pages: 65 – 88

DOI: https://dx.doi.org/10.4310/AJM.2021.v25.n1.a5

Authors

Lev Borisov (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)

Zengrui Han (School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China)

Chengxi Wang (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)

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.

Keywords

hypergeometric systems, Gamma series, Euler characteristics pairing, twisted sectors, $K$‑theory, duality

2010 Mathematics Subject Classification

13D09, 14J32, 14J33, 14M25, 33C99

Received 16 November 2019

Accepted 14 April 2020