  Let M_g be the moduli space of stable curves of genus g >= 2. Let D_i be the
irreducible component of the boundary of M_g such that general points of D_i
correspond to stable curves with one node of type i. Let M_g^0 be the set of
stable curves that have at most one node of type i>0. Let d_i be the class of
D_i in Pic(M_g)_Q and h the Hodge class on M_g. In this paper, we will prove a
sharp slope inequality for general stable fibrations. Namely, if $C$ is a
complete curve on M_g^0, then ( (8g+4)h - g d_0 - \sum_{i=1}^{[g/2]} 4i(g-i)
d_i . C ) >= 0. As an application, we can prove effective Bogomolov's
conjecture for general stable fibrations.
