Generating Functions for Hurwitz-Hodge Integrals

Abstract

In this paper we describe explicit generating functions for a large class of Hurwitz-Hodge integrals. These are integrals of tautological classes on moduli spaces of admissible covers, a (stackily) smooth compactification of the Hurwitz schemes. Admissible covers and their tautological classes are interesting mathematical objects on their own, but recently they have proved to be a useful tool for the study of the tautological ring of the moduli space of curves, and the orbifold Gromov-Witten theory of DM stacks. Our main tool is Atiyah-Bott localization: its underlying philosophy is to translate an interesting geometric problem into a purely combinatorial one.

17 pages, 2 figures

References in corpus (3)

• Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
• Higher-genus Gromov-Witten invariants as genus 0 invariants of symmetric products
• Towards the geometry of double Hurwitz numbers

Cited by in corpus (5)

• Crepant resolution conjecture in all genera for type A singularities
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture
• Gerby Localization, Z_3-Hodge Integrals and the GW Theory of C^3/Z_3
• Evaluating tautological classes using only Hurwitz numbers