Hurwitz numbers and intersections on moduli spaces of curves

Abstract

This article is an extended version of preprint math.AG/9902104. We find an explicit formula for the number of topologically different ramified coverings of a sphere by a genus g surface with only one complicated branching point in terms of Hodge integrals over the moduli space of genus g curves with marked points.

30 pages (AMSTeX). Minor typos are corrected

References in corpus (4)

• Hodge integrals and Hurwitz numbers via virtual localization
• Stable maps and branch divisors
• Recursions, formulas, and graph-theoretic interpretations of ramified coverings of the sphere by surfaces of genus 0 and 1
• Enumerative geometry of plane curves of low genus

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