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

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.

59pages. This paper is a revision of the integral structure part of the preprint arXiv:0712.2204. More details on toric mirror symmetry have been added, v2: added a reference, v3: There were logical gaps in the argument of the conformal Batyrev ring in Section 3.2.3; mistakes in Section 3.2.3 removed and Proposition 4.4 modified using the work of Adolphson

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