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arXiv · 0705.0070

The Cox Ring of $\bar{M}_{0,6}$

Ana-Maria Castravet
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Abstract

We prove that the Cox ring of $\bar{M}_{0,6}$, the moduli space 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 $\bar{M}_3$, the moduli space of stable, genus 3 curves, via morphisms 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 $\bar{M}_{0,6}$ being generated by the above mentioned divisors.

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Ana-Maria Castravet. 2008-09-16. The Cox Ring of $\bar{M}_{0,6}$. https://arxiv.org/abs/0705.0070

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