Gamma integral structure for an invertible polynomial of chain type

TL;DR

This paper introduces a Gamma integral structure for invertible polynomials of chain type and proves its equivalence to the natural integral structure via mirror symmetry, extending Iritani's framework.

Contribution

It defines the Gamma integral structure for chain type polynomials and verifies its correspondence with the natural structure through mirror symmetry, confirming Iritani's Gamma conjecture.

Findings

Gamma integral structure is well-defined for chain type polynomials.

The structure is identified with the natural integral structure via mirror isomorphism.

Supports Iritani's Gamma conjecture in this context.

Abstract

The notion of the Gamma integral structure for the quantum cohomology of an algebraic variety was introduced by Iritani, Katzarkov-Kontsevich-Pantev. In this paper, we define the Gamma integral structure for an invertible polynomial of chain type. Based on the $\Gamma$-conjecture by Iritani, we prove that the Gamma integral structure is identified with the natural integral structure for the Berglund-H\"{u}bsch transposed polynomial by the mirror isomorphism.