Generating Functions for Hurwitz-Hodge Integrals

Details Generating Functions for Hurwitz-Hodge Integrals Generating Functions for Hurwitz-Hodge Integrals

2006-08-23

arxiv.org/abs/math/0608590v1

Mathematics

Algebraic Geometry

17 pages, 2 figures

Scientific paper

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.

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