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

Ian P. Goulden·David M. Jackson·Ravi Vakil
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Abstract

We give a short and direct proof of the $λ_g$-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.

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Ian P. Goulden, David M. Jackson, Ravi Vakil. 2006-04-12. A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves. https://arxiv.org/abs/math/0604297

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