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
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C^2/Z_3 和 Hurwitz-Hodge 积分的轨道量子上同调
DOI：
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发表时间：
2005
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通讯作者：
R. Pandharipande
中科院分区：
文献类型：
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作者：
J. Bryan;T. Graber;R. Pandharipande
设Z_3以非平凡的相反特征标作用于C^2。设X =[C^2/Z_3]为轨道商，Y为唯一的临界分辨率.我们证明了X和Y的等变亏格为0的Gromov-Witten势在变量变化后是相等的--验证了对（X，Y）的Crepant归结猜想。我们的计算涉及霍奇积分三角赫维茨空间是独立的利益。在一个完备的附录中，我们导出了这些Hurwitz-Hodge积分的封闭公式。
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.