{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TNSDFBO25HOZFPAEFZQGYW6ZYD","short_pith_number":"pith:TNSDFBO2","schema_version":"1.0","canonical_sha256":"9b643285dae9dd92bc042e606c5bd9c0d929cd2bc22e743497f786d1630efbc4","source":{"kind":"arxiv","id":"1803.01357","version":1},"attestation_state":"computed","paper":{"title":"On the Infinitesimal Torelli theorem for regular surfaces with very ample canonical divisor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Igor Reider","submitted_at":"2018-03-04T14:03:10Z","abstract_excerpt":"Let $X$ be a smooth compact complex surface subject to the following conditions:\n  (i) the canonical line bundle $\\mathcal{O}_X(K_X) $ is very ample,\n  (ii) the irregularity $q(X): = h^1(\\mathcal{O}_X) =0$,\n  (iii) $X$ contains no rational normal curves of degree $\\leq (p_g-1)$,\n  (iv) the multiplication map $m_2: Sym^2(H^0(\\mathcal{O}_X(K_X))) \\longrightarrow H^0 (\\mathcal{O}_X (2K_X))$ is surjective.\n  It is shown that the Infinitesimal Torelli holds for such $X$.\n  Our proof is based on the study of the cup-product\n  $$ H^1 (\\Theta_X) \\longrightarrow (\\mathcal{O}_X(K_X))^{\\ast} \\otimes H^1 "},"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":"1803.01357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-04T14:03:10Z","cross_cats_sorted":[],"title_canon_sha256":"9899a173784208fc90d71a08260bcd9f415858eca2e78d258a4dd4ad7e8bc452","abstract_canon_sha256":"3c3cdd7c953be1d50604ca64c29ade099c73c79870ecb8c0533c906ba87b5b38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:00.930246Z","signature_b64":"DHls48jz6CuXXFkYPIaWkBXGV57ZHsauBcLQtEDPMa9QFrTPyKn7vsudKOOLQC3SDJri7+rjcqm8UptaKz0tAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b643285dae9dd92bc042e606c5bd9c0d929cd2bc22e743497f786d1630efbc4","last_reissued_at":"2026-05-18T00:22:00.929595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:00.929595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Infinitesimal Torelli theorem for regular surfaces with very ample canonical divisor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Igor Reider","submitted_at":"2018-03-04T14:03:10Z","abstract_excerpt":"Let $X$ be a smooth compact complex surface subject to the following conditions:\n  (i) the canonical line bundle $\\mathcal{O}_X(K_X) $ is very ample,\n  (ii) the irregularity $q(X): = h^1(\\mathcal{O}_X) =0$,\n  (iii) $X$ contains no rational normal curves of degree $\\leq (p_g-1)$,\n  (iv) the multiplication map $m_2: Sym^2(H^0(\\mathcal{O}_X(K_X))) \\longrightarrow H^0 (\\mathcal{O}_X (2K_X))$ is surjective.\n  It is shown that the Infinitesimal Torelli holds for such $X$.\n  Our proof is based on the study of the cup-product\n  $$ H^1 (\\Theta_X) \\longrightarrow (\\mathcal{O}_X(K_X))^{\\ast} \\otimes H^1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01357","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":""},"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":"1803.01357","created_at":"2026-05-18T00:22:00.929684+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.01357v1","created_at":"2026-05-18T00:22:00.929684+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01357","created_at":"2026-05-18T00:22:00.929684+00:00"},{"alias_kind":"pith_short_12","alias_value":"TNSDFBO25HOZ","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"TNSDFBO25HOZFPAE","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"TNSDFBO2","created_at":"2026-05-18T12:32:53.628368+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/TNSDFBO25HOZFPAEFZQGYW6ZYD","json":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD.json","graph_json":"https://pith.science/api/pith-number/TNSDFBO25HOZFPAEFZQGYW6ZYD/graph.json","events_json":"https://pith.science/api/pith-number/TNSDFBO25HOZFPAEFZQGYW6ZYD/events.json","paper":"https://pith.science/paper/TNSDFBO2"},"agent_actions":{"view_html":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD","download_json":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD.json","view_paper":"https://pith.science/paper/TNSDFBO2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.01357&json=true","fetch_graph":"https://pith.science/api/pith-number/TNSDFBO25HOZFPAEFZQGYW6ZYD/graph.json","fetch_events":"https://pith.science/api/pith-number/TNSDFBO25HOZFPAEFZQGYW6ZYD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD/action/storage_attestation","attest_author":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD/action/author_attestation","sign_citation":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD/action/citation_signature","submit_replication":"https://pith.science/pith/TNSDFBO25HOZFPAEFZQGYW6ZYD/action/replication_record"}},"created_at":"2026-05-18T00:22:00.929684+00:00","updated_at":"2026-05-18T00:22:00.929684+00:00"}