{"paper":{"title":"Effective transitive actions of the unitary group on quotients of Hopf manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexander Isaev","submitted_at":"2016-07-27T05:19:30Z","abstract_excerpt":"In our article of 2002 joint with N. Kruzhilin we showed that every connected complex manifold of dimension $n\\ge 2$ that admits an effective transitive action by holomorphic transformations of the unitary group ${\\rm U}_n$ is biholomorphic to the quotient of a Hopf manifold by the action of ${\\mathbb Z}_m$ for some integer $m$ satisfying $(n,m)=1$. In this note, we complement the above result with an explicit description of all effective transitive actions of ${\\rm U}_n$ on such quotients, which provides an answer to a 10-year old question."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07964","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"}