Real and integral structures in quantum cohomology I: toric orbifolds

Details Real and integral structures in quantum cohomology I: toric orbifolds Real and integral structures in quantum cohomology I: toric orbifolds

2007-12-13

arxiv.org/abs/0712.2204v3

Mathematics

Algebraic Geometry

66 pages, v2: many minor changes, v3: many changes, references added, the results on the integral structure and mirror symmetr

Scientific paper

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.

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