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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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: 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
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