{"paper":{"title":"Quasi-complete intersections in P2 and syzygies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Philippe Ellia","submitted_at":"2019-02-14T16:10:22Z","abstract_excerpt":"Let C \\in P2 be a reduced, singular curve of degree d and equation f = 0. Let \\Sigma denote the jacobian subscheme of C. We have 0 -> E -> 3.O -> I_\\Sigma(d-1) -> 0 (the surjection is given by the partials of f). We study the relationships between the Betti numbers of the module H^0_*(E) and the integers, d; \\tau, where \\tau = deg(\\Sigma). We observe that our results apply to any quasi-complete intersection of type (s; s; s)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05472","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"}