{"paper":{"title":"Quotients of del Pezzo surfaces of degree 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrey Trepalin","submitted_at":"2017-09-06T21:27:48Z","abstract_excerpt":"Let $\\Bbbk$ be any field of characteristic zero, $X$ be a del Pezzo surface of degree~$2$ and $G$ be a group acting on $X$. In this paper we study $\\Bbbk$-rationality questions for the quotient surface $X / G$. If there are no smooth $\\Bbbk$-points on $X / G$ then $X / G$ is obviously non-$\\Bbbk$-rational.\n  Assume that the set of smooth $\\Bbbk$-points on the quotient is not empty. We find a list of groups, such that the quotient surface can be non-$\\Bbbk$-rational. For these groups we construct examples of both $\\Bbbk$-rational and non-$\\Bbbk$-rational quotients of both $\\Bbbk$-rational and n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02006","kind":"arxiv","version":3},"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"}