Nef divisors in codimension one on the moduli space of stable curves

Details Nef divisors in codimension one on the moduli space of stable curves Nef divisors in codimension one on the moduli space of stable curves

2000-05-02

arxiv.org/abs/math/0005012v4

Mathematics

Algebraic Geometry

30 pages, simplify the main result, add questions

Scientific paper

Let M_g be the moduli space of smooth curves of genus g >= 3, and \bar{M}_g the Deligne-Mumford compactification in terms of stable curves. Let \bar{M}_g^{[1]} be an open set of \bar{M}_g 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 \bar{M}_g is nef over \bar{M}_g^{[1]}, that is, (D . C) >= 0 for all irreducible curves C on \bar{M}_g with C \cap \bar{M}_g^{[1]} \not= \emptyset.

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