The orbifold quantum cohomology of C2/Z3 and Hurwitz-Hodge integrals
Jim Bryan, Tom Graber, Rahul Pandharipande
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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