{"paper":{"title":"Quotients of del Pezzo surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrey Trepalin","submitted_at":"2019-06-07T11:59:15Z","abstract_excerpt":"Let $\\Bbbk$ be any field of characteristic zero, $X$ be a del Pezzo surface and $G$ be a finite subgroup in $\\operatorname{Aut}(X)$. In this paper we study when the quotient surface $X / G$ can be non-rational over $\\Bbbk$. Obviously, if there are no smooth $\\Bbbk$-points on $X / G$ then it is not $\\Bbbk$-rational. Therefore under assumption that the set of smooth $\\Bbbk$-points on $X / G$ is not empty we show that there are few possibilities for non-$\\Bbbk$-rational quotients.\n  The quotients of del Pezzo surfaces of degree $2$ and greater are considered in the author's previous papers. In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04030","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"}