{"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. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5535","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"}