{"paper":{"title":"On the X-rank with respect to linear projections of projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Edoardo Ballico","submitted_at":"2009-12-24T11:15:56Z","abstract_excerpt":"In this paper we improve the known bound for the $X$-rank $R_{X}(P)$ of an element $P\\in {\\mathbb{P}}^N$ in the case in which $X\\subset {\\mathbb P}^n$ is a projective variety obtained as a linear projection from a general $v$-dimensional subspace $V\\subset {\\mathbb P}^{n+v}$. Then, if $X\\subset {\\mathbb P}^n$ is a curve obtained from a projection of a rational normal curve $C\\subset {\\mathbb P}^{n+1}$ from a point $O\\subset {\\mathbb P}^{n+1}$, we are able to describe the precise value of the $X$-rank for those points $P\\in {\\mathbb P}^n$ such that $R_{X}(P)\\leq R_{C}(O)-1$ and to improve the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4834","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"}