{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MCVCQLZSIWHNICZLCW7O77WJD6","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":"855c1b34090df78e68290babc22a8dae5746c2a0f80342dba932cd7fb5db1ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-28T17:46:15Z","title_canon_sha256":"7cbb65e020aac9f126ca1d1bb53a0b369a3cd11035e8a5aa6849e070002d499d"},"schema_version":"1.0","source":{"id":"1203.6323","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6323","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6323v6","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6323","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"MCVCQLZSIWHN","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MCVCQLZSIWHNICZL","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MCVCQLZS","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:e7eeccc7b5b99b3688289d6a50c806ea5124874b146be32bbd6e513df970e10d","target":"graph","created_at":"2026-05-18T02:39:09Z","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":"We study the deformation theory of a Q-Fano 3-fold with only terminal singularities. First, we show that the Kuranishi space of a Q-Fano 3-fold is smooth. Second, we show that every Q-Fano 3-fold with only \"ordinary\" terminal singularities is Q-smoothable, that is, it can be deformed to a Q-Fano 3-fold with only quotient singularities. Finally, we prove Q-smoothability of a Q-Fano 3-fold assuming the existence of a Du Val anticanonical element. As an application, we get the genus bound for primary Q-Fano 3-folds with Du Val anticanonical elements.","authors_text":"Taro Sano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-28T17:46:15Z","title":"On deformations of Q-Fano threefolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6323","kind":"arxiv","version":6},"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":"sha256:3b7c0ec9ad255d23902840d3f1e21a123329b8a68f4ad57a670563c131f9085b","target":"record","created_at":"2026-05-18T02:39:09Z","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":"855c1b34090df78e68290babc22a8dae5746c2a0f80342dba932cd7fb5db1ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-28T17:46:15Z","title_canon_sha256":"7cbb65e020aac9f126ca1d1bb53a0b369a3cd11035e8a5aa6849e070002d499d"},"schema_version":"1.0","source":{"id":"1203.6323","kind":"arxiv","version":6}},"canonical_sha256":"60aa282f32458ed40b2b15beeffec91fb4de20517d8ac19dbed15c90d6ebf8cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60aa282f32458ed40b2b15beeffec91fb4de20517d8ac19dbed15c90d6ebf8cd","first_computed_at":"2026-05-18T02:39:09.349551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:09.349551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eO4TzYzCtkfo/6ysjM7vhRtMYl9mc65JmV5BJtaOhcdiQKK35/Dhej9Oo6uFQdc4DPzqs0mKIzxfs8k4OxAZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:09.350273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6323","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b7c0ec9ad255d23902840d3f1e21a123329b8a68f4ad57a670563c131f9085b","sha256:e7eeccc7b5b99b3688289d6a50c806ea5124874b146be32bbd6e513df970e10d"],"state_sha256":"216c28bac1734f91f052f647cf55dc9e7675e1acd6614f25861218e31dd207ee"}