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

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.

26 pages; revisions in the proof of Lemma 2.21

Cited by in corpus (5)

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