{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:UEGPBDTCGLHXASTJUNBNAYPFBH","short_pith_number":"pith:UEGPBDTC","schema_version":"1.0","canonical_sha256":"a10cf08e6232cf704a69a342d061e509e3c0013233b4a548787100788bcbbac6","source":{"kind":"arxiv","id":"0909.2763","version":3},"attestation_state":"computed","paper":{"title":"Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Russo, Paltin Ionescu","submitted_at":"2009-09-15T10:34:32Z","abstract_excerpt":"Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geometry of the variety of lines through a general point, we characterize scrolls among dual defective manifolds. This leads to an optimal bound for the dual defect, which improves results due to Ein. We disc"},"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":"0909.2763","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-09-15T10:34:32Z","cross_cats_sorted":[],"title_canon_sha256":"28a440630f502eeeb35b432f791df35e5904bb1f403b5ca899c996bbc6a4eb74","abstract_canon_sha256":"d0940b82b18c7b927349002ac224ca079e5d9b5adabc3978acd65cd6eff2e746"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:04.200914Z","signature_b64":"oAOIl+8mU7EJuyjSzDE5cu2sPFZ0sc3Rl9g8vKM7pGUtXPuPvOX2YAp+JROWZLpJilodQwxI8mnmHmImWG8ZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a10cf08e6232cf704a69a342d061e509e3c0013233b4a548787100788bcbbac6","last_reissued_at":"2026-05-18T03:46:04.200155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:04.200155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Russo, Paltin Ionescu","submitted_at":"2009-09-15T10:34:32Z","abstract_excerpt":"Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geometry of the variety of lines through a general point, we characterize scrolls among dual defective manifolds. This leads to an optimal bound for the dual defect, which improves results due to Ein. We disc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2763","kind":"arxiv","version":3},"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":"0909.2763","created_at":"2026-05-18T03:46:04.200276+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.2763v3","created_at":"2026-05-18T03:46:04.200276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2763","created_at":"2026-05-18T03:46:04.200276+00:00"},{"alias_kind":"pith_short_12","alias_value":"UEGPBDTCGLHX","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"UEGPBDTCGLHXASTJ","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"UEGPBDTC","created_at":"2026-05-18T12:26:02.257875+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/UEGPBDTCGLHXASTJUNBNAYPFBH","json":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH.json","graph_json":"https://pith.science/api/pith-number/UEGPBDTCGLHXASTJUNBNAYPFBH/graph.json","events_json":"https://pith.science/api/pith-number/UEGPBDTCGLHXASTJUNBNAYPFBH/events.json","paper":"https://pith.science/paper/UEGPBDTC"},"agent_actions":{"view_html":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH","download_json":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH.json","view_paper":"https://pith.science/paper/UEGPBDTC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.2763&json=true","fetch_graph":"https://pith.science/api/pith-number/UEGPBDTCGLHXASTJUNBNAYPFBH/graph.json","fetch_events":"https://pith.science/api/pith-number/UEGPBDTCGLHXASTJUNBNAYPFBH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH/action/storage_attestation","attest_author":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH/action/author_attestation","sign_citation":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH/action/citation_signature","submit_replication":"https://pith.science/pith/UEGPBDTCGLHXASTJUNBNAYPFBH/action/replication_record"}},"created_at":"2026-05-18T03:46:04.200276+00:00","updated_at":"2026-05-18T03:46:04.200276+00:00"}