{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YWSDYN36DOF6OADNRWN3EJZYZ3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0c11fa07022d11137877f4511d2d3b14dac25f3ea338ebe420d5494f586a376b","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-05T14:37:29Z","title_canon_sha256":"a6d6d3dc1d2459d8500b74ff8319ff28857f5a8d83eac887350f20217482c73c"},"schema_version":"1.0","source":{"id":"1508.01089","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01089","created_at":"2026-05-18T01:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01089v2","created_at":"2026-05-18T01:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01089","created_at":"2026-05-18T01:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"YWSDYN36DOF6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YWSDYN36DOF6OADN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YWSDYN36","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:95658e392754c78ae6e01e71aa31448c294be6ddfab117915a874411759a15cb","target":"graph","created_at":"2026-05-18T01:35:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $X$ be a Fano threefold and $\\C ^* \\times X\\rightarrow X$ an algebraic action. Then $X$ has a $S^1$-invariant K\\\"ahler structure and the corresponding $S^1$-action admits an equivariant moment map which is at the same time a perfect Bott-Morse function. We will initiate a program to classify the Fano threefolds with semi-free ${\\mathbb C}^*$-actions using Morse theory and the holomorphic Lefschetz fixed point formula as the main tools. In this paper we give a complete list of all possible Fano threefolds without \"interior isolated fixed points\" for any semi-free ${\\mathbb C}^*$-action. For","authors_text":"Dan Zaffran, Qilin Yang","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-05T14:37:29Z","title":"On Fano threefolds with semi-free ${\\mathbb C}^*$-actions, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01089","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:545fd08f54763a1bcf2cd170fec9f804da1b2eb530c4c91a20e3fc91da15fffc","target":"record","created_at":"2026-05-18T01:35:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0c11fa07022d11137877f4511d2d3b14dac25f3ea338ebe420d5494f586a376b","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-05T14:37:29Z","title_canon_sha256":"a6d6d3dc1d2459d8500b74ff8319ff28857f5a8d83eac887350f20217482c73c"},"schema_version":"1.0","source":{"id":"1508.01089","kind":"arxiv","version":2}},"canonical_sha256":"c5a43c377e1b8be7006d8d9bb22738ced8b4eee738c07f3a0b52e9a62c8af350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5a43c377e1b8be7006d8d9bb22738ced8b4eee738c07f3a0b52e9a62c8af350","first_computed_at":"2026-05-18T01:35:04.456241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:04.456241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YuucgrXwtHoP+hpNQNQFP+UupPUW9nSBEx4zK+vzGoowP+ujrIBKb2M73WM7khijQMDJJBw8YL3R0HJXtgX0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:04.456728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01089","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:545fd08f54763a1bcf2cd170fec9f804da1b2eb530c4c91a20e3fc91da15fffc","sha256:95658e392754c78ae6e01e71aa31448c294be6ddfab117915a874411759a15cb"],"state_sha256":"05538f39914ce30186634cbdb15c693e54b1a5018d772af35bbf6591a5df4ced"}