{"paper":{"title":"The Cox Ring of $\\bar{M}_{0,6}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Ana-Maria Castravet","submitted_at":"2007-05-01T04:34:25Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0070","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}