Nef Divisors in Codimension One on the Moduli Space of Stable Curves |
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Authors: | Atsushi Moriwaki |
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Affiliation: | (1) Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan |
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Abstract: | Let Mg be the moduli space of smooth curves of genus g 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 -divisor D on M¯g is nef over M¯g[1], that is, (D · C) 0 for all irreducible curves C on M¯g with C M¯g[1] . |
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Keywords: | Nef divisor Moduli space Stable curve |
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