{"paper":{"title":"Orbits of actions of group superschemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"A.N.Zubkov, V.A.Bovdi","submitted_at":"2022-02-18T19:08:47Z","abstract_excerpt":"Working over an algebraically closed field $\\Bbbk$, we prove that all orbits of a left action of an algebraic group superscheme $G$ on a superscheme $X$ of finite type are locally closed. Moreover, such an orbit $Gx$, where $x$ is a $\\Bbbk$-point of $X$, is closed if and only if $G_{ev}x$ is closed in $X_{ev}$, or equivalently, if and only if $G_{res}x$ is closed in $X_{res}$. Here $G_{ev}$ is the largest purely even group super-subscheme of $G$ and $G_{res}$ is $G_{ev}$ regarded as a group scheme. Similarly, $X_{ev}$ is the largest purely even super-subscheme of $X$ and $X_{res}$ is $X_{ev}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.09384","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.09384/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}