A sharp slope inequality for general stable fibrations of curves

1996/01/05 by Moriwaki, Atsushi
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9601003

Abstract

Let M_g be the moduli space of stable curves of genus g >= 2. Let D_i be the irreducible component of the boundary of M_g such that general points of D_i correspond to stable curves with one node of type i. Let M_g⁰ be the set of stable curves that have at most one node of type i>0. Let d_i be the class of D_i in Pic(M_g)_Q and h the Hodge class on M_g. In this paper, we will prove a sharp slope inequality for general stable fibrations. Namely, if C is a complete curve on M_g⁰, then ( (8g+4)h - g d₀ - ∑_i=1^[g/2] 4i(g-i) d_i . C ) >= 0. As an application, we can prove effective Bogomolov's conjecture for general stable fibrations.

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