Hodge-type integrals on moduli spaces of admissible covers
Abstract
Description
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
This is the version published by Geometry & Topology Monographs on 21 September 2007