{"paper":{"title":"Interpolation for normal bundles of general curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atanas Atanasov, David Yang, Eric Larson","submitted_at":"2015-09-05T18:13:17Z","abstract_excerpt":"Given n general points p_1, p_2,..., p_n in P^r, it is natural to ask when there exists a curve C \\subset P^r, of degree d and genus g, passing through p_1, p_2,..., p_n. In this paper, we give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle N_C of a general nonspecial curve of degree d and genus g in P^r (with d >= g + r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H^0(N_C(-D)) = 0 or H^1(N_C(-D)) = 0), with exa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01724","kind":"arxiv","version":3},"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"}