{"paper":{"title":"Projective varieties of maximal sectional regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Euisung Park, Markus Brodmann, Peter Schenzel, Wanseok Lee","submitted_at":"2015-02-06T01:42:48Z","abstract_excerpt":"We study projective varieties $X \\subset \\mathbb{P}^r$ of dimension $n \\geq 2$, of codimension $c \\geq 3$ and of degree $d \\geq c + 3$ that are of maximal sectional regularity, i.e. varieties for which the Castelnuovo-Mumford regularity $\\reg (\\mathcal{C})$ of a general linear curve section is equal to $d -c+1$, the maximal possible value (see \\cite{GruLPe}). As one of the main results we classify all varieties of maximal sectional regularity. If $X$ is a variety of maximal sectional regularity, then either (a) it is a divisor on a rational normal $(n+1)$-fold scroll $Y \\subset \\mathbb{P}^{n+3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01769","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"}