# The Cox Ring of $ar{M} {0,6}$ - Mathematics > Algebraic Geometry

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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 sectionscorresponding to the boundary divisors and divisors which are pull-backs of thehyperelliptic 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 byidentifying 3 pairs of points. In particular, this gives a self-contained proofof Hassett and Tschinkel-s result about the effective cone of $\bar{M} {0,6}$being generated by the above mentioned divisors.

Author: ** Ana-Maria Castravet**

Source: https://arxiv.org/