Crepant resolutions of weighted projective spaces and quantum deformations

Details Crepant resolutions of weighted projective spaces and quantum deformations Crepant resolutions of weighted projective spaces and quantum deformations

2006-10-20

arxiv.org/abs/math/0610617v2

Mathematics

Algebraic Geometry

Exposition improved, new title, typos corrected. The section concerning the model for the orbifold Chow ring has been removed

Scientific paper

We compare the Chen-Ruan cohomology ring of the weighted projective spaces $\IP(1,3,4,4)$ and $\IP(1,...,1,n)$ with the cohomology ring of their crepant resolutions. In both cases, we prove that the Chen-Ruan cohomology ring is isomorphic to the quantum corrected cohomology ring of the crepant resolution after suitable evaluation of the quantum parameters. For this, we prove a formula for the Gromov-Witten invariants of the resolution of a transversal ${\rm A}_3$ singularity.

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