Nef divisors in codimension one on the moduli space of stable curves
Atsushi Moriwaki
Abstract
Let Mg be the moduli space of smooth curves of genus g >= 3, and Mg the Deligne-Mumford compactification in terms of stable curves. Let Mg[1] be an open set of Mg consisting of stable curves of genus g with one node at most. In this paper, we determine the necessary and sufficient condition to guarantee that a Q-divisor D on Mg is nef over Mg[1], that is, (D . C) >= 0 for all irreducible curves C on Mg with C Mg[1] = .
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