Crepant resolutions of weighted projective spaces and quantum deformations

2006/10/20 by Samuel Boissière, Boissiere, Samuel, Étienne Mann +3
Mathematics · #14E15 #14F45 #14N35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0610617

openalex publication_date 2006/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \rm A₃ singularity.

Citations

• Cohomology ring of crepant resolutions of orbifolds
• Cohomologie quantique orbifolde des espaces projectifs a poids
• Orbifold Cohomology of ADE-singularities
• A model for the orbifold Chow ring of weighted projective spaces

Related

• The cohomological crepant resolution conjecture for P(1,3,4,4)
• Quantum Cohomology and Crepant Resolutions: A Conjecture
• Chen-Ruan cohomology of ADE singularities
• The Crepant Resolution Conjecture for Type A Surface Singularities
• The Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphisms