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 (3)

• 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 (3)

• Gerby Localization, Z_3-Hodge Integrals and the GW Theory of C^3/Z_3
• Generating Functions for Hurwitz-Hodge Integrals
• Evaluating tautological classes using only Hurwitz numbers