The orbifold quantum cohomology of C^2/Z_3 and Hurwitz-Hodge integrals

Abstract

Let Z_3 act on C^2 by non-trivial opposite characters. Let X =[C^2/Z_3] 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.

arXiv comment25 pages

References in corpus (1)

• Topological Orbifold Models and Quantum Cohomology Rings

Cited by in corpus (5)

• Computing Genus-Zero Twisted Gromov-Witten Invariants
• The Crepant Transformation Conjecture for Toric Complete Intersections
• Orbifold Hurwitz numbers and Eynard-Orantin invariants
• Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds
• Crepant resolution and the holomorphic anomaly equation for C^3/Z_3