The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture

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We define the dimension 2g-1 Faber-Hurwitz Chow/homology classes on the moduli space of curves, parametrizing curves expressible as branched covers of P^1 with given ramification over infinity and sufficiently many fixed ramification points elsewhere. Degeneration of the target and judicious localization expresses such classes in terms of localization trees weighted by ``top intersections'' of tautological classes and genus 0 double Hurwitz numbers. This identity of generating series can be inverted, yielding a ``combinatorialization'' of top intersections of psi-classes. As genus 0 double Hurwitz numbers with at most 3 parts over infinity are well understood, we obtain Faber's Intersection Number Conjecture for up to 3 parts, and an approach to the Conjecture in general (bypassing the Virasoro Conjecture). We also recover other geometric results in a unified manner, including Looijenga's theorem, the socle theorem for curves with rational tails, and the hyperelliptic locus in terms of kappa_{g-2}.
45 pages, 6 figures

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Algebraic Geometry, Combinatorics, Primary 14H10, Secondary 05E99, 14K30

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http://salesiana.dossiersoluciones.com/handle/123456789/119374

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611659
 http://arxiv.org/abs/math/0611659

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arXiv