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We show that the canonical ring R(C, \\omega_C)= \\oplus_{k \\geq 0} H^0(C, \\omega_C^k is generated in degree 1 if C is 3-connected and not (honestly) hyperelliptic; we show moreover that R(C, L)=\\oplus_{k \\geq 0} H^0(C,L^k)$ is generated in degree 1 if C is reduced with planar singularities and L is an invertible sheaf such that deg L_{|B} \\geq 2p_a(B)+1 for every B \\subseteq C."},"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":"1107.5535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-27T16:49:18Z","cross_cats_sorted":[],"title_canon_sha256":"e28bf6aa5ca729673f6fc19c8bb67ec0d026cf3cd6f67a44f2f18596ed0928eb","abstract_canon_sha256":"7038d64eedfec942269e3be46ca44f1d4b0172fccafdbf3aabed35e9d6ced53a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:23.304125Z","signature_b64":"fe2f6+We3BeX+G6npUp0gHMCwZQUTeaUHTDhst1peGbIkWL0wGEKe0Ijjfhv7nawD5JL14KDw3Y2n2bbwx83Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"279704625064fbe41eda5b81db5381b4615f6f72ec4dcae4976d84210d8f2093","last_reissued_at":"2026-05-18T03:27:23.303605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:23.303605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The canonical ring of a 3-connected curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elisa Tenni, Marco Franciosi","submitted_at":"2011-07-27T16:49:18Z","abstract_excerpt":"Let C be a projective curve either reduced with planar singularities or contained in a smooth algebraic surface. 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