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

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

2009-03-08

arxiv.org/abs/0903.1463v3

Adv. Math. 222 (2009), no.3, 1016-1079

Mathematics

Algebraic Geometry

59pages. This paper is a revision of the integral structure part of the preprint arXiv:0712.2204. More details on toric mirror

Scientific paper

10.1016/j.aim.2009.05.016

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.

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