Abstract
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 -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 ].
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