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Nef Divisors in Codimension One on the Moduli Space of Stable Curves

Published online by Cambridge University Press:  04 December 2007

Atsushi Moriwaki
Atsushi Moriwaki
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan. E-mail: moriwaki@kusm.kyoto-u.ac.jp
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Abstract

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Let Mg be the moduli space of smooth curves of genus g [ges ] 3, and M¯g the Deligne-Mumford compactification in terms of stable curves. Let M¯g[1] be an open set of 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 $\open Q$-divisor D on M¯g is nef over M¯g[1], that is, (D · C) [ges ] 0 for all irreducible curves C on M¯g with C ∩ M¯g[1] ≠ [empty ].

Keywords

Nef divisorModuli spaceStable curve
Type
Research Article
Information
Compositio Mathematica , Volume 132 , Issue 2 , June 2002 , pp. 191 - 228
Copyright
© 2002 Kluwer Academic Publishers