{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FPQV6U3P4YU4IRGSDTVR6P7ZYV","short_pith_number":"pith:FPQV6U3P","schema_version":"1.0","canonical_sha256":"2be15f536fe629c444d21ceb1f3ff9c541c0807d1ade07b78b1a73e7ae8d4c34","source":{"kind":"arxiv","id":"1607.07964","version":2},"attestation_state":"computed","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.07964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-27T05:19:30Z","cross_cats_sorted":[],"title_canon_sha256":"f0f5c559c545b47ff7440ece209ccb6638bfd632ae5644d62556b354cc54615c","abstract_canon_sha256":"83c4df212a1ca0cbdbb3f043b62755551c2380c8e90a267e2ee283afe03e9c48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:56.705442Z","signature_b64":"44gn0SwH6b97wd9FostmenbJj4hVkAHVRlFb+Aji6z7dOMCACSlpMaz2aamThutgFayKTGdcZUIheyFUcdtpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2be15f536fe629c444d21ceb1f3ff9c541c0807d1ade07b78b1a73e7ae8d4c34","last_reissued_at":"2026-05-18T01:03:56.704773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:56.704773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.07964","created_at":"2026-05-18T01:03:56.704875+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.07964v2","created_at":"2026-05-18T01:03:56.704875+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07964","created_at":"2026-05-18T01:03:56.704875+00:00"},{"alias_kind":"pith_short_12","alias_value":"FPQV6U3P4YU4","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FPQV6U3P4YU4IRGS","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FPQV6U3P","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV","json":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV.json","graph_json":"https://pith.science/api/pith-number/FPQV6U3P4YU4IRGSDTVR6P7ZYV/graph.json","events_json":"https://pith.science/api/pith-number/FPQV6U3P4YU4IRGSDTVR6P7ZYV/events.json","paper":"https://pith.science/paper/FPQV6U3P"},"agent_actions":{"view_html":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV","download_json":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV.json","view_paper":"https://pith.science/paper/FPQV6U3P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.07964&json=true","fetch_graph":"https://pith.science/api/pith-number/FPQV6U3P4YU4IRGSDTVR6P7ZYV/graph.json","fetch_events":"https://pith.science/api/pith-number/FPQV6U3P4YU4IRGSDTVR6P7ZYV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV/action/storage_attestation","attest_author":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV/action/author_attestation","sign_citation":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV/action/citation_signature","submit_replication":"https://pith.science/pith/FPQV6U3P4YU4IRGSDTVR6P7ZYV/action/replication_record"}},"created_at":"2026-05-18T01:03:56.704875+00:00","updated_at":"2026-05-18T01:03:56.704875+00:00"}