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

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- by Gavril Farkas and Angela Gibney PDF
- Trans. Amer. Math. Soc.
**355**(2003), 1183-1199 Request permission

## Abstract:

We compute the Mori cones of the moduli spaces $\overline M_{g,n}$ 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 $\overline M_g$ 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 $\overline M_{0,6}$, thus verifying Fulton’s conjecture for this space. Using this description we obtain a classification of all the fibrations of $\overline M_{0,6}$.## References

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## Additional Information

**Gavril Farkas**- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
- Email: gfarkas@umich.edu
**Angela Gibney**- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
- MR Author ID: 689485
- Email: agibney@umich.edu
- Received by editor(s): February 25, 2002
- Published electronically: November 7, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**355**(2003), 1183-1199 - MSC (2000): Primary 14H10
- DOI: https://doi.org/10.1090/S0002-9947-02-03165-3
- MathSciNet review: 1938752