{"paper":{"title":"Dependent subsets of embedded projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico","submitted_at":"2019-05-20T14:54:27Z","abstract_excerpt":"Let $X\\subset \\mathbb {P}^r$ be an integral and non-degenerate variety. Set $n:= \\dim (X)$. Let $\\rho (X)''$ be the maximal integer such that every zero-dimensional scheme $Z\\subset X$ smoothable in $X$ is linearly independent. We prove that $X$ is linearly normal if $\\rho (X)''\\ge \\lceil (r+2)/2\\rceil$ and that $\\rho (X)'' < 2\\lceil (r+1)/(n+1)\\rceil$, unless either $n=r$ or $X$ is a rational normal curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08149","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"}