Generating Functions for Hurwitz-Hodge Integrals
Abstract
Description
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
17 pages, 2 figures