Real and integral structures in quantum cohomology I: toric orbifolds
Abstract
We study real and integral structures in the space of solutions to the quantum differential equations. First we show that, under mild conditions, any real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry near the large radius limit. Secondly, we use mirror symmetry to calculate the "most natural" integral structure in quantum cohomology of toric orbifolds. We show that the integral structure pulled back from the singularity B-model is described only in terms of topological data in the A-model; K-group and a characteristic class. Using integral structures, we give a natural explanation why the quantum parameter should specialize to a root of unity in Ruan's crepant resolution conjecture.
Keywords
Cite
@article{arxiv.0712.2204,
title = {Real and integral structures in quantum cohomology I: toric orbifolds},
author = {Hiroshi Iritani},
journal= {arXiv preprint arXiv:0712.2204},
year = {2009}
}
Comments
66 pages, v2: many minor changes, v3: many changes, references added, the results on the integral structure and mirror symmetry (except for real structures) of this preprint have been revised in the paper arXiv:0903.1463