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

Let M _g 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] .