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

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

2005-10-16

arxiv.org/abs/math/0510335v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

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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