# The mori cones of moduli spaces of pointed curves of small genus

@article{Farkas2001TheMC,
title={The mori cones of moduli spaces of pointed curves of small genus},
author={G. Farkas and A. Gibney},
journal={Transactions of the American Mathematical Society},
year={2001},
volume={355},
pages={1183-1199}
}
• Published 2001
• Mathematics
• Transactions of the American Mathematical Society
We compute the Mori cones of the moduli spaces M g,n of n pointed stable curves of genus g, when g and n are relatively small. For instance we show that for g < 14 every curve in Mg is equivalent to an effective combination of the components of the locus of curves with 3g - 4 nodes. We completely describe the cone of nef divisors for the space M 0,6 , thus verifying Fulton's conjecture for this space. Using this description we obtain a classification of all the fibrations of M 0,6 .
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