{"paper":{"title":"Closed H-orbits in G-varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"Michael Bate","submitted_at":"2012-11-05T15:13:26Z","abstract_excerpt":"Let G be a linear algebraic group, H a subgroup of G and X a G-variety. This paper explores the connection between G-orbits and H-orbits in X, concentrating in particular on the question of when we have the implications G.x closed in X implies H.x closed in X, and vice versa. Some of the general results found in this paper are then used in the special case where G and H are reductive and X is affine to extend two classical results of Luna from characteristic zero to arbitrary characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0885","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"}