Hodge-type integrals on moduli spaces of admissible covers

Abstract

We study Hodge Integrals on Moduli Spaces of Admissible Covers. Motivation for this work comes from Bryan and Pandharipande's recent work on the local GW theory of curves, where analogouos intersection numbers, computed on Moduli Spaces of Relative Stable Maps, are the structure coefficients for a Topological Quantum Field Theory. Admissible Covers provide an alternative compactification of the Moduli Space of Maps, that is smooth and doesn't contain boundary components of excessive dimension. A parallel, yet different, TQFT, can then be constructed. In this paper we compute, using localization, the relevant Hodge integrals for admissible covers of a pointed sphere of degree 2 and 3, and formulate a conjecture for general degree. In genus 0, we recover the well-known Aspinwall Morrison formula in GW theory.

This is the version published by Geometry & Topology Monographs on 21 September 2007

References in corpus (2)

• Hurwitz numbers and intersections on moduli spaces of curves
• On Hurwitz numbers and Hodge integrals

Cited by in corpus (6)

• Crepant resolution conjecture in all genera for type A singularities
• Generating Functions for Hurwitz-Hodge Integrals
• Hyperelliptic classes are rigid and extremal in genus two
• A TQFT of Intersection Numbers on Moduli Spaces of Admissible Covers
• An example of crepant resolution conjecture in two steps
• Evaluating tautological classes using only Hurwitz numbers