Effective cones of quotients of moduli spaces of stable -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 , the moduli space of -pointed stable genus zero curves, and let be the quotient of by the action of on the last marked points. The cones of effective divisors , , are calculated. Using this, upper bounds for the cones generated by divisors with moving linear systems are calculated, , along with the induced bounds on the cones of ample divisors of and . As an application, the cone is analyzed in detail.

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Additional Information

**William F. Rulla**

Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602

Email:
rulla@math.uga.edu

DOI:
https://doi.org/10.1090/S0002-9947-06-03851-7

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.