Nef divisors in codimension one on the moduli space of stable curves
Algebraic Geometry
2007-05-23 v4
Abstract
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.
Keywords
Cite
@article{arxiv.math/0005012,
title = {Nef divisors in codimension one on the moduli space of stable curves},
author = {Atsushi Moriwaki},
journal= {arXiv preprint arXiv:math/0005012},
year = {2007}
}
Comments
30 pages, simplify the main result, add questions