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Generating Functions for Hurwitz-Hodge Integrals

Renzo Cavalieri
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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.

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Renzo Cavalieri. 2006-08-23. Generating Functions for Hurwitz-Hodge Integrals. https://arxiv.org/abs/math/0608590

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