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We prove that if $A$ contains no rational curves then the automorphism group $G:=Aut(W)$ of $W$ is Jordan. That means that there is a positive integer $J=J(W)$ such that every finite subgroup $\\mathcal{B}$ of ${G}$ contains a commutative subgroup $\\mathcal{A}$ such that $\\mathcal{A}$ is normal in $\\mathcal{B}$ and the index $[\\mathcal{B}:\\mathcal{A}] \\le J$ ."},"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":"1705.07523","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-22T00:04:01Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d80bd1dca6856a54414c67a46d94c14cadd09c8c94f27b5cda6e015b9cdbbe77","abstract_canon_sha256":"c4d40f7871b0a946c9574550835e3ad9346c44870567be9f0fa6cf5d89eafa0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:40.796646Z","signature_b64":"aYEF8xnYPiByPjsyKlD5lugG4IcMjbhju92cCb5G7NL8xNnC41cQEXjvlH3LoaxRHcyPbCR5hf0ADT2MGtg8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"799749d118e0a8a6492768331ce9f974fa288e3d1afdd95d80255bca2488fa60","last_reissued_at":"2026-05-18T00:28:40.795958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:40.795958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jordan properties of automorphism groups of certain open algebraic varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Tatiana Bandman, Yuri G. Zarhin","submitted_at":"2017-05-22T00:04:01Z","abstract_excerpt":"Let $W$ be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that $W$ is birational to a product of a smooth projective variety $A$ and the projective line. We prove that if $A$ contains no rational curves then the automorphism group $G:=Aut(W)$ of $W$ is Jordan. That means that there is a positive integer $J=J(W)$ such that every finite subgroup $\\mathcal{B}$ of ${G}$ contains a commutative subgroup $\\mathcal{A}$ such that $\\mathcal{A}$ is normal in $\\mathcal{B}$ and the index $[\\mathcal{B}:\\mathcal{A}] \\le J$ ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07523","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":"1705.07523","created_at":"2026-05-18T00:28:40.796063+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.07523v2","created_at":"2026-05-18T00:28:40.796063+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07523","created_at":"2026-05-18T00:28:40.796063+00:00"},{"alias_kind":"pith_short_12","alias_value":"PGLUTUIY4CUK","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PGLUTUIY4CUKMSJH","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PGLUTUIY","created_at":"2026-05-18T12:31:37.085036+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/PGLUTUIY4CUKMSJHNAZRZ2PZOT","json":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT.json","graph_json":"https://pith.science/api/pith-number/PGLUTUIY4CUKMSJHNAZRZ2PZOT/graph.json","events_json":"https://pith.science/api/pith-number/PGLUTUIY4CUKMSJHNAZRZ2PZOT/events.json","paper":"https://pith.science/paper/PGLUTUIY"},"agent_actions":{"view_html":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT","download_json":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT.json","view_paper":"https://pith.science/paper/PGLUTUIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.07523&json=true","fetch_graph":"https://pith.science/api/pith-number/PGLUTUIY4CUKMSJHNAZRZ2PZOT/graph.json","fetch_events":"https://pith.science/api/pith-number/PGLUTUIY4CUKMSJHNAZRZ2PZOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT/action/storage_attestation","attest_author":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT/action/author_attestation","sign_citation":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT/action/citation_signature","submit_replication":"https://pith.science/pith/PGLUTUIY4CUKMSJHNAZRZ2PZOT/action/replication_record"}},"created_at":"2026-05-18T00:28:40.796063+00:00","updated_at":"2026-05-18T00:28:40.796063+00:00"}