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

Published electronically:
November 7, 2002

MathSciNet review:
1938752

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Abstract: We compute the Mori cones of the moduli spaces of pointed stable curves of genus , when and are relatively small. For instance we show that for every curve in is equivalent to an effective combination of the components of the locus of curves with nodes. We completely describe the cone of nef divisors for the space , thus verifying Fulton's conjecture for this space. Using this description we obtain a classification of all the fibrations of .

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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

Email:
agibney@umich.edu

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

Received by editor(s):
February 25, 2002

Published electronically:
November 7, 2002

Article copyright:
© Copyright 2002
American Mathematical Society