The orbifold quantum cohomology of C²/Z₃ and Hurwitz-Hodge integrals

2005/10/16 by Jim Bryan, Bryan, Jim, Tom Graber +3
Mathematics · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0510335

openalex publication_date 2005/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Z₃ act on C² by non-trivial opposite characters. Let X =[C²/Z₃] be the orbifold quotient, and let Y be the unique crepant resolution. We show the equivariant genus 0 Gromov-Witten potentials of X and Y are equal after a change of variables -- verifying the Crepant Resolution Conjecture for the pair (X,Y). Our computations involve Hodge integrals on trigonal Hurwitz spaces which are of independent interest. In a self contained Appendix, we derive closed formulas for these Hurwitz-Hodge integrals.

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