English

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)].

Keywords

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}
}
R2 v1 2026-06-21T09:12:31.747Z