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}
}
  • G. Farkas, A. Gibney
  • 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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