The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits
Abstract
We first describe a canonical mirror partner (B-model) of the small quantum orbifold cohomology of weighted projective spaces (A-model) in the framework of differential equations: we attach to the A-model (resp. B-model) a D-module on the torus and we show that these two D-modules are isomorphic. This makes the A and B-models mirror partners and yields, in this situation, an explicit and finer version of a recent result of Iritani. Then we study, using the theory of the Kashiwara-Malgrange filtration, their degenerations at the origin and we apply our results to the construction of (classical, limit, logarithmic) Frobenius manifolds.
Keywords
Cite
@article{arxiv.0909.4063,
title = {The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits},
author = {Antoine Douai and Etienne Mann},
journal= {arXiv preprint arXiv:0909.4063},
year = {2012}
}
Comments
35 pages, Supersedes the paper arXiv:0806.2011, v2: minor corrections, v3:minor corrections accepted for publication in Geometriae Dedicata