Effective divisors on M_g and a counterexample to the Slope Conjecture

2002/09/13 by Gavril Farkas, Farkas, Gavril, Mihnea Popa +1
Mathematics · #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10

paper · pdf · doi:10.48550/arxiv.math/0209171

7 pages, minor expository changes

arxiv created 2002/09/24 · arxiv updated 2009/11/30

Abstract

We prove two statements on the slopes of effective divisors on the moduli space of stable curves of genus g: first that the Harris-Morrison Slope Conjecture fails for g=10 and second, that in order to compute the slope of the moduli space of curves for g≤ 23, one only has to consider the coefficients of the Hodge class and that of the boundary divisor δ₀ in the expansion of the relevant divisors. We conjecture that the same statement holds in arbitrary genus.

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