Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture
Algebraic Geometry
2007-09-03 v1
Abstract
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)].
Cite
@article{arxiv.0708.4244,
title = {Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture},
author = {Jim Bryan and Amin Gholampour},
journal= {arXiv preprint arXiv:0708.4244},
year = {2007}
}