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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Cox ring of $ \overline{M}_{0,6}$


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: We prove that the Cox ring of the moduli space $ \overline{M}_{0,6}$, of stable rational curves with $ 6$ marked points, is finitely generated by sections corresponding to the boundary divisors and divisors which are pull-backs of the hyperelliptic locus in $ \overline{M}_3$ via morphisms $ \rho:\overline{M}_{0,6}\rightarrow \overline{M}_3$ that send a $ 6$-pointed rational curve to a curve with $ 3$ nodes by identifying $ 3$ pairs of points. In particular this gives a self-contained proof of Hassett and Tschinkel's result about the effective cone of $ \overline{M}_{0,6}$ 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
PII: S 0002-9947(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.