A sharp slope inequality for general stable fibrations of curves
alg-geom
2015-06-30 v1 Algebraic Geometry
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_g^0 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 is a complete curve on M_g^0, then ( (8g+4)h - g d_0 - \sum_{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.
Cite
@article{arxiv.alg-geom/9601003,
title = {A sharp slope inequality for general stable fibrations of curves},
author = {Atsushi Moriwaki},
journal= {arXiv preprint arXiv:alg-geom/9601003},
year = {2015}
}
Comments
18 pages (with 1 figure by epic.sty), AmSLaTeX version 1.2 (LaTeX2e)