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

2006/04/12 by Goulden, Ian P., Jackson, David M., Vakil, Ravi
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary 14H10 #Secondary 05E99

paper · doi:10.48550/arxiv.math/0604297

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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