Crepant resolutions of weighted projective spaces and quantum deformations

Abstract

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 ${\mathrm{A}}_3$ 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)

References in corpus (11)

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• Cohomology ring of crepant resolutions of orbifolds
• The Crepant Resolution Conjecture for Type A Surface Singularities
• Mirror Symmetry on Kummer Type K3 Surfaces
• Cohomologie quantique orbifolde des espaces projectifs a poids
• Orbifold Cohomology of ADE-singularities
• The Quantum Orbifold Cohomology of Weighted Projective Spaces
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• Orbifold Cohomology of A Wreath Product Orbifold
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Cited by in corpus (6)

• On the Crepant Resolution Conjecture in the Local Case
• Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples
• The Quantum Orbifold Cohomology of Weighted Projective Spaces
• The cohomological crepant resolution conjecture for P(1,3,4,4)
• The Full Orbifold $K$-theory of Abelian Symplectic Quotients
• Torsion in the full orbifold K-theory of abelian symplectic quotients