A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves

Abstract

We give a short and direct proof of the ${\lambda }_g$-Conjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the ``polynomiality'' of Hurwitz numbers, from which we pick off the lowest degree terms. The proof is independent of Gromov-Witten theory. We briefly describe the philosophy behind our general approach to intersection numbers and how it may be extended to other intersection number conjectures.

References in corpus (7)

• Hurwitz numbers and intersections on moduli spaces of curves
• On the tautological ring of $\M _g$
• An algebro-geometric proof of Witten's conjecture
• Virasoro constraints and the Chern classes of the Hodge bundle
• Three questions in Gromov-Witten theory
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Virasoro constraints for target curves

Cited by in corpus (5)

• The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers
• Gerby Localization, Z_3-Hodge Integrals and the GW Theory of C^3/Z_3
• Generating Functions for Hurwitz-Hodge Integrals
• Polynomial recursion formula for linear Hodge integrals
• Evaluating tautological classes using only Hurwitz numbers