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

Abstract

Let G be the group A_4 or Z_2xZ_2. We compute the integral of λ_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)].

References in corpus (2)

• The Crepant Resolution Conjecture for Type A Surface Singularities
• Generating Functions for Hurwitz-Hodge Integrals

Cited by in corpus (8)

• The Crepant Transformation Conjecture for Toric Complete Intersections
• On the Crepant Resolution Conjecture in the Local Case
• Crepant resolution conjecture in all genera for type A singularities
• On the mathematics and physics of high genus invariants of [C^3/Z_3]
• Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples
• Crepant resolutions and open strings II
• Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
• The Quantum McKay Correspondence for Singularities of type D