{"paper":{"title":"The rationality problem for forms of $\\overline{M_{0, n}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.AG","authors_text":"Mathieu Florence, Zinovy Reichstein","submitted_at":"2017-09-17T17:51:32Z","abstract_excerpt":"Let $X$ be a del Pezzo surface of degree $5$ defined over a field $F$. A theorem of Yu. I. Manin and P. Swinnerton-Dyer asserts that every Del Pezzo surface of degree $5$ is rational. In this paper we generalize this result as follows. Recall that del Pezzo surfaces of degree $5$ over a field $F$ are precisely the twisted $F$-forms of the moduli space $\\overline{M_{0, 5}}$ of stable curves of genus $0$ with $5$ marked points. Suppose $n \\geq 5$ is an integer, and $F$ is an infinite field of characteristic $\\neq 2$. It is easy to see that every twisted $F$-form of $\\overline{M_{0, n}}$ is unira"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05698","kind":"arxiv","version":1},"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"}