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

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

2006-04-12

arxiv.org/abs/math/0604297v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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