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There are many more than expected.\n  Along the way, we conjecture that for every projective birational morphism $\\pi\\colon X\\to Y$ of smooth varieties, and every line bundle $A$ on $X$ that is ample over $Y$, the higher direct image sheaf $R^j\\pi_*(\\Omega^i_X\\otimes A)$ is zero for every $j>0$ and $"},"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":"2302.08142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-02-16T08:28:13Z","cross_cats_sorted":[],"title_canon_sha256":"ee23c79121a019a0536b98a549105865590669d3899cef00febc4473e35cd411","abstract_canon_sha256":"d376f9a54346f7eac06d0231f9e98aae681c90e2fd6e0124529947b508d3a6b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:42:34.877173Z","signature_b64":"aGxtdhRtRMIw12v/rqgLRvpju0OqD3Syu8bs1kOu2w123i0S1yVThm4ajtiAc7/MDitiq70Fbp36vcHu08cVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5a8e68668c6fbdd595f1e8b5dc538e09a519812748d4081b6859c271fff6dde","last_reissued_at":"2026-07-05T05:42:34.876783Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:42:34.876783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bott vanishing for Fano 3-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Burt Totaro","submitted_at":"2023-02-16T08:28:13Z","abstract_excerpt":"Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that $H^j(X,\\Omega^i_X\\otimes L)=0$ for every $j>0$, $i\\geq 0$, and $L$ ample. This holds for toric varieties, but not for most other varieties.\n  We classify the smooth Fano 3-folds that satisfy Bott vanishing. There are many more than expected.\n  Along the way, we conjecture that for every projective birational morphism $\\pi\\colon X\\to Y$ of smooth varieties, and every line bundle $A$ on $X$ that is ample over $Y$, the higher direct image sheaf $R^j\\pi_*(\\Omega^i_X\\otimes A)$ is zero for every $j>0$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08142","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.08142/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2302.08142","created_at":"2026-07-05T05:42:34.876840+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.08142v1","created_at":"2026-07-05T05:42:34.876840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08142","created_at":"2026-07-05T05:42:34.876840+00:00"},{"alias_kind":"pith_short_12","alias_value":"6WUONBTIY355","created_at":"2026-07-05T05:42:34.876840+00:00"},{"alias_kind":"pith_short_16","alias_value":"6WUONBTIY3552WK7","created_at":"2026-07-05T05:42:34.876840+00:00"},{"alias_kind":"pith_short_8","alias_value":"6WUONBTI","created_at":"2026-07-05T05:42:34.876840+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.16325","citing_title":"Images of toric variety and amplified endomorphism of weak Fano threefolds","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C","json":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C.json","graph_json":"https://pith.science/api/pith-number/6WUONBTIY3552WK7D2FV3RJY4C/graph.json","events_json":"https://pith.science/api/pith-number/6WUONBTIY3552WK7D2FV3RJY4C/events.json","paper":"https://pith.science/paper/6WUONBTI"},"agent_actions":{"view_html":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C","download_json":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C.json","view_paper":"https://pith.science/paper/6WUONBTI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.08142&json=true","fetch_graph":"https://pith.science/api/pith-number/6WUONBTIY3552WK7D2FV3RJY4C/graph.json","fetch_events":"https://pith.science/api/pith-number/6WUONBTIY3552WK7D2FV3RJY4C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C/action/storage_attestation","attest_author":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C/action/author_attestation","sign_citation":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C/action/citation_signature","submit_replication":"https://pith.science/pith/6WUONBTIY3552WK7D2FV3RJY4C/action/replication_record"}},"created_at":"2026-07-05T05:42:34.876840+00:00","updated_at":"2026-07-05T05:42:34.876840+00:00"}