An integral structure in quantum cohomology and mirror symmetry for toric orbifolds

TL;DR

This paper introduces an integral structure in orbifold quantum cohomology linked to the K-group and Gamma-class, demonstrating its compatibility with mirror symmetry for toric orbifolds and explaining specializations in Ruan's crepant resolution conjecture.

Contribution

It establishes a new integral structure in orbifold quantum cohomology and shows its correspondence with the Landau-Ginzburg model under mirror symmetry for toric orbifolds.

Findings

Integral structure matches with Landau-Ginzburg model for toric orbifolds

Provides explanation for root of unity specialization in Ruan's conjecture

Connects orbifold quantum cohomology with mirror symmetry via integral structures

Abstract

We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the Gamma-class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for the Landau-Ginzburg model under mirror symmetry. By assuming the existence of an integral structure, we give a natural explanation for the specialization to a root of unity in Y. Ruan's crepant resolution conjecture.