{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IK5FFHRBVI5EMLZITCZYIRH33A","short_pith_number":"pith:IK5FFHRB","schema_version":"1.0","canonical_sha256":"42ba529e21aa3a462f2898b38444fbd83ea3c7c27094e3af7dd4762856978c01","source":{"kind":"arxiv","id":"1107.0579","version":1},"attestation_state":"computed","paper":{"title":"On the canonical ring of curves and surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marco Franciosi","submitted_at":"2011-07-04T09:59:34Z","abstract_excerpt":"Let C be a curve (possibly non reduced or reducible) lying on a smooth algebraic surface. We show that the canonical ring R(C, \\omega_C) is generated in degree 1 if C is numerically 4-connected, not hyperelliptic and even (i.e. with K_C of even degree on every component). As a corollary we show that on a smooth algebraic surface of general type with p_g(S)>0 and q(S)=0 the canonical ring R(S, K_S) is generated in degree \\leq 3 if there exists a curve C in |K_S| numerically 3-connected and not hyperelliptic."},"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":"1107.0579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-04T09:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"f7b865a546c10231ff8b52bf64e55d0e9088b2fea02cbd336bd3e844090ad85a","abstract_canon_sha256":"212edf7bb7868ca0a32d806195e93b74cfbccd6587fe92ad1331b7c0fb9408a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:53.736794Z","signature_b64":"9HCds6fu5AQEtrLd7K1+7RH5TEzbJzxJbzwc2sCaLhFGFQuETTvq4gNpALMh1vTItvkBMyDbUJroSN9XYS8nAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42ba529e21aa3a462f2898b38444fbd83ea3c7c27094e3af7dd4762856978c01","last_reissued_at":"2026-05-18T04:18:53.736295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:53.736295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the canonical ring of curves and surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marco Franciosi","submitted_at":"2011-07-04T09:59:34Z","abstract_excerpt":"Let C be a curve (possibly non reduced or reducible) lying on a smooth algebraic surface. We show that the canonical ring R(C, \\omega_C) is generated in degree 1 if C is numerically 4-connected, not hyperelliptic and even (i.e. with K_C of even degree on every component). As a corollary we show that on a smooth algebraic surface of general type with p_g(S)>0 and q(S)=0 the canonical ring R(S, K_S) is generated in degree \\leq 3 if there exists a curve C in |K_S| numerically 3-connected and not hyperelliptic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0579","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":"1107.0579","created_at":"2026-05-18T04:18:53.736393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.0579v1","created_at":"2026-05-18T04:18:53.736393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0579","created_at":"2026-05-18T04:18:53.736393+00:00"},{"alias_kind":"pith_short_12","alias_value":"IK5FFHRBVI5E","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"IK5FFHRBVI5EMLZI","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"IK5FFHRB","created_at":"2026-05-18T12:26:30.835961+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/IK5FFHRBVI5EMLZITCZYIRH33A","json":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A.json","graph_json":"https://pith.science/api/pith-number/IK5FFHRBVI5EMLZITCZYIRH33A/graph.json","events_json":"https://pith.science/api/pith-number/IK5FFHRBVI5EMLZITCZYIRH33A/events.json","paper":"https://pith.science/paper/IK5FFHRB"},"agent_actions":{"view_html":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A","download_json":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A.json","view_paper":"https://pith.science/paper/IK5FFHRB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.0579&json=true","fetch_graph":"https://pith.science/api/pith-number/IK5FFHRBVI5EMLZITCZYIRH33A/graph.json","fetch_events":"https://pith.science/api/pith-number/IK5FFHRBVI5EMLZITCZYIRH33A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A/action/storage_attestation","attest_author":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A/action/author_attestation","sign_citation":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A/action/citation_signature","submit_replication":"https://pith.science/pith/IK5FFHRBVI5EMLZITCZYIRH33A/action/replication_record"}},"created_at":"2026-05-18T04:18:53.736393+00:00","updated_at":"2026-05-18T04:18:53.736393+00:00"}