Crepant resolutions of weighted projective spaces and quantum deformations
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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.
Exposition improved, new title, typos corrected. The section concerning the model for the orbifold Chow ring has been removed (appears now in our new preprint 0709.4559)
Exposition improved, new title, typos corrected. The section concerning the model for the orbifold Chow ring has been removed (appears now in our new preprint 0709.4559)