{"paper":{"title":"On curves lying on a rational normal surface scroll","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Euisung Park, Wanseok Lee","submitted_at":"2018-08-09T06:39:02Z","abstract_excerpt":"In this paper, we study the minimal free resolution of non-ACM divisors $X$ of a smooth rational normal surface scroll $S=S(a_1 ,a_2 ) \\subset \\mathbb{P}^r$. Our main result shows that for $a_2 \\geq 2a_1 -1$, there exists a nice decomposition of the Betti table of $X$ as a sum of much simpler Betti tables. As a by-product of our results, we obtain a complete description of the graded Betti numbers of $X$ for the cases where $S=S(1,r-2)$ for some $r \\geq 3$ and $S=S(2,r-3)$ for some $r \\geq 6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03038","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"}