The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits

Details The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits

2009-09-22

arxiv.org/abs/0909.4063v2

Mathematics

Algebraic Geometry

33 pages, Supersedes the paper arXiv:0806.2011, v2: minor corrections

Scientific paper

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.

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