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

Jim Bryan·Tom Graber·Rahul Pandharipande
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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.

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Jim Bryan, Tom Graber, Rahul Pandharipande. 2005-10-16. The orbifold quantum cohomology of C^2/Z_3 and Hurwitz-Hodge integrals. https://arxiv.org/abs/math/0510335

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