The Cox ring of $\overline {M}_{0,6}$
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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.References
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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
- MR Author ID: 730339
- Email: noni@math.umass.edu, noni@math.arizona.edu
- Received by editor(s): May 4, 2007
- Received by editor(s) in revised form: September 24, 2007
- Published electronically: January 28, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 3851-3878
- MSC (2000): Primary 14E30, 14H10, 14H51, 14M99
- DOI: https://doi.org/10.1090/S0002-9947-09-04641-8
- MathSciNet review: 2491903