Towards the ample cone of \overline{}_{,}

@article{Gibney2000TowardsTA,
  title={Towards the ample cone of \overline\{\}_\{,\}},
  author={A. Gibney and S. Keel and I. Morrison},
  journal={Journal of the American Mathematical Society},
  year={2000},
  volume={15},
  pages={273-294}
}
In this paper we study the ample cone of the moduli space $\mgn$ of stable $n$-pointed curves of genus $g$. Our motivating conjecture is that a divisor on $\mgn$ is ample iff it has positive intersection with all 1-dimensional strata (the components of the locus of curves with at least $3g+n-2$ nodes). This translates into a simple conjectural description of the cone by linear inequalities, and, as all the 1-strata are rational, includes the conjecture that the Mori cone is polyhedral and… Expand
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