{"paper":{"title":"Secant spaces and syzygies of special line bundles on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Sernesi, Marian Aprodu","submitted_at":"2014-03-11T09:47:04Z","abstract_excerpt":"On a special line bundle $L$ on a projective curve $C$ we introduce a geometric condition called $(\\Delta_q)$. When $L=K_C$ this condition implies gon$(C) \\ge q+2$. For an arbitrary special $L$ we show that $(\\Delta_3)$ implies that $L$ has the well-known property $(M_3)$, generalizing a similar result proved by Voisin in the case $L=K_C$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2516","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"}