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Transactions of the American Mathematical Society

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



Effective cones of quotients of moduli spaces of stable $ n$-pointed curves of genus zero

Author: William F. Rulla
Journal: Trans. Amer. Math. Soc. 358 (2006), 3219-3237
MSC (2000): Primary 14E05, 14H10; Secondary 14E30
Published electronically: February 20, 2006
MathSciNet review: 2216265
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Abstract: Let $ X_n := \overline{M}_{0,n}$, the moduli space of $ n$-pointed stable genus zero curves, and let $ X_{n,m}$ be the quotient of $ X_n$ by the action of $ \mathcal{S}_{n-m}$ on the last $ n-m$ marked points. The cones of effective divisors $ \overline{NE}^1(X_{n,m})$, $ m = 0,1,2$, are calculated. Using this, upper bounds for the cones $ Mov(X_{n,m})$ generated by divisors with moving linear systems are calculated, $ m = 0,1$, along with the induced bounds on the cones of ample divisors of $ \overline{M}_g$ and $ \overline{M}_{g,1}$. As an application, the cone $ \overline{NE}^1(\overline{M}_{2,1})$ is analyzed in detail.

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Additional Information

William F. Rulla
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602

Keywords: Moduli space, rational curve, birational geometry, classification of morphisms/rational maps
Received by editor(s): December 5, 2003
Received by editor(s) in revised form: September 9, 2004
Published electronically: February 20, 2006
Additional Notes: This paper is a product of a VIGRE seminar on $\overline{M}_{0,n}$ conducted by V. Alexeev at the University of Georgia, Athens, during the Spring of 2002. Thanks to S. Keel for posing the question motivating the paper, and to him, R. Varley, and E. Izadi for help and advice. Thanks also to the referee for many valuable comments. PORTA was used in calculating several examples. Xfig was used for the figures.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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