Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture

Details Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture

2007-08-30

arxiv.org/abs/0708.4244v1

Mathematics

Algebraic Geometry

Scientific paper

Let G be the group A_4 or Z_2xZ_2. We compute the integral of \lambda_g on the Hurwitz locus H_G\subset M_g of curves admitting a degree 4 cover of P^1 having monodromy group G. We compute the generating functions for these integrals and write them as a trigonometric expression summed over the positive roots of the E_6 and D_4 root systems respectively. As an application, we prove the Crepant Resolution Conjecture for the orbifolds [C^3/A_4] and [C^3/(Z_2xZ_2)].

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