{"paper":{"title":"Resolutions of General Canonical Curves on Rational Normal Scrolls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Bopp, Michael Hoff","submitted_at":"2015-05-27T09:27:11Z","abstract_excerpt":"Let $C\\subset \\mathbb{P}^{g-1}$ be a general curve of genus $g$ and let $k$ be a positive integer such that the Brill-Noether number $\\rho(g,k,1)\\geq 0$ and $g > k+1$. The aim of this short note is to study the relative canonical resolution of $C$ on a rational normal scroll swept out by a $g^1_k=|L|$ with $L\\in W^1_k(C)$ general. We show that the bundle of quadrics appearing in the relative canonical resolution is unbalanced if and only if $\\rho>0$ and $(k-\\rho-\\frac{7}{2})^2-2k+\\frac{23}{4}>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07235","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"}