The Cox ring of

Author:
Ana-Maria Castravet

Journal:
Trans. Amer. Math. Soc. **361** (2009), 3851-3878

MSC (2000):
Primary 14E30, 14H10, 14H51, 14M99

Published electronically:
January 28, 2009

MathSciNet review:
2491903

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Cox ring of the moduli space , of stable rational curves with marked points, is finitely generated by sections corresponding to the boundary divisors and divisors which are pull-backs of the hyperelliptic locus in via morphisms that send a -pointed rational curve to a curve with nodes by identifying pairs of points. In particular this gives a self-contained proof of Hassett and Tschinkel's result about the effective cone of being generated by the above mentioned divisors.

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Additional Information

**Ana-Maria Castravet**

Affiliation:
Department of Mathematics, University of Massachusetts at Amherst, Amherst, Massachusetts 01003

Address at time of publication:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721

Email:
noni@math.umass.edu, noni@math.arizona.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-09-04641-8

Keywords:
Cox rings,
Mori Dream Spaces,
moduli spaces of stable curves

Received by editor(s):
May 4, 2007

Received by editor(s) in revised form:
September 24, 2007

Published electronically:
January 28, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.