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

Authors:
Gavril Farkas and Angela Gibney

Journal:
Trans. Amer. Math. Soc. **355** (2003), 1183-1199

MSC (2000):
Primary 14H10

DOI:
https://doi.org/10.1090/S0002-9947-02-03165-3

Published electronically:
November 7, 2002

MathSciNet review:
1938752

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Abstract | References | Similar Articles | Additional Information

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 $\overline M_{0,6}$.

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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

Article copyright:
© Copyright 2002
American Mathematical Society