{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:I6BYKVSKIKTW3FQ7IRIZIYDRHO","short_pith_number":"pith:I6BYKVSK","schema_version":"1.0","canonical_sha256":"478385564a42a76d961f44519460713ba6863c95b5904fd719aedf68d480ddc8","source":{"kind":"arxiv","id":"1510.02964","version":2},"attestation_state":"computed","paper":{"title":"Some results on deformations of sections of vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, Gian Pietro Pirola","submitted_at":"2015-10-10T17:38:03Z","abstract_excerpt":"Let $E$ be a vector bundle on a smooth complex projective variety $X$. We study the family of sections $s_t\\in H^0(E\\otimes L_t)$ where $L_t\\in Pic^0(X)$ is a family of topologically trivial line bundle and $L_0=\\mathcal O_X,$ that is, we study deformations of $s=s_0$. By applying the approximation theorem of Artin [2] we give a transversality condition that generalizes the semi-regularity of an effective Cartier divisor. Moreover, we obtain another proof of the Severi-Kodaira-Spencer theorem [4]. We apply our results to give a lower bound to the continuous rank of a vector bundle as defined b"},"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":"1510.02964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-10T17:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"7864e4def7602d23f0fdf4eb0a0cd6bddcc294276de1756590c83a77e917fcbc","abstract_canon_sha256":"c35d03d78e21d508d540d11f9fb051cec85c7253905ab2ff671e0bf0375357e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:18.627126Z","signature_b64":"J/COdYwrryOQO6Dz9osjk8LGgWa7yxAf+DgRUOuZvwCW+AHgMET1KVhhK60KmwicNOL1Arpkx0UlAcvrXfqIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"478385564a42a76d961f44519460713ba6863c95b5904fd719aedf68d480ddc8","last_reissued_at":"2026-05-18T01:17:18.626628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:18.626628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some results on deformations of sections of vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, Gian Pietro Pirola","submitted_at":"2015-10-10T17:38:03Z","abstract_excerpt":"Let $E$ be a vector bundle on a smooth complex projective variety $X$. We study the family of sections $s_t\\in H^0(E\\otimes L_t)$ where $L_t\\in Pic^0(X)$ is a family of topologically trivial line bundle and $L_0=\\mathcal O_X,$ that is, we study deformations of $s=s_0$. By applying the approximation theorem of Artin [2] we give a transversality condition that generalizes the semi-regularity of an effective Cartier divisor. Moreover, we obtain another proof of the Severi-Kodaira-Spencer theorem [4]. We apply our results to give a lower bound to the continuous rank of a vector bundle as defined b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02964","kind":"arxiv","version":2},"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":"1510.02964","created_at":"2026-05-18T01:17:18.626710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02964v2","created_at":"2026-05-18T01:17:18.626710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02964","created_at":"2026-05-18T01:17:18.626710+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6BYKVSKIKTW","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6BYKVSKIKTW3FQ7","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6BYKVSK","created_at":"2026-05-18T12:29:25.134429+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/I6BYKVSKIKTW3FQ7IRIZIYDRHO","json":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO.json","graph_json":"https://pith.science/api/pith-number/I6BYKVSKIKTW3FQ7IRIZIYDRHO/graph.json","events_json":"https://pith.science/api/pith-number/I6BYKVSKIKTW3FQ7IRIZIYDRHO/events.json","paper":"https://pith.science/paper/I6BYKVSK"},"agent_actions":{"view_html":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO","download_json":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO.json","view_paper":"https://pith.science/paper/I6BYKVSK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02964&json=true","fetch_graph":"https://pith.science/api/pith-number/I6BYKVSKIKTW3FQ7IRIZIYDRHO/graph.json","fetch_events":"https://pith.science/api/pith-number/I6BYKVSKIKTW3FQ7IRIZIYDRHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO/action/storage_attestation","attest_author":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO/action/author_attestation","sign_citation":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO/action/citation_signature","submit_replication":"https://pith.science/pith/I6BYKVSKIKTW3FQ7IRIZIYDRHO/action/replication_record"}},"created_at":"2026-05-18T01:17:18.626710+00:00","updated_at":"2026-05-18T01:17:18.626710+00:00"}