  We prove two statements on the slopes of effective divisors on the moduli
space of stable curves of genus g: first that the Harris-Morrison Slope
Conjecture fails for g=10 and second, that in order to compute the slope of the
moduli space of curves for g\leq 23, one only has to consider the coefficients
of the Hodge class and that of the boundary divisor \delta_0 in the expansion
of the relevant divisors. We conjecture that the same statement holds in
arbitrary genus.

Algebraic Geometry