  The moduli space $\M_{g,n}$ of $n-$pointed stable curves of genus $g$ is
stratified by the topological type of the curves being parametrized: the
closure of the locus of curves with $k$ nodes has codimension $k$. The one
dimensional components of this stratification are smooth rational curves (whose
numerical equivalence classes are) called F-curves. The F-conjecture asserts
that a divisor on $\M_{g,n}$ is ample if and only if it positively intersects
the $F-$curves.
  In this paper the F-conjecture on $\M_{g,n}$ is reduced to showing that
certain divisors in $\M_{0,N}$ for $N \leq g+n$ are equivalent to the sum of
the canonical divisor plus an effective divisor supported on the boundary. As
an application of the reduction, numerical criteria are given which if
satisfied by a divisor $D$ on $\M_g$, show that $D$ is ample. Additionally, an
algorithm is described to check that a given divisor is ample.
  Using a computer program called Nef Wizard, written by Daniel Krashen
(http://www.yale.edu/users/dkrashen/nefwiz), one can use the criteria and the
algorithm to verify the conjecture for low genus. This is done on $\M_g$ for $g
\le 24$, more than doubling the known cases of the conjecture and showing it is
true for the first genus such that $\M_g$ is known to be of general type.
