{"paper":{"title":"Grassmann secants, identifiability, and linear systems of tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Edoardo Ballico, Luca Chiantini, Maria Virginia Catalisano","submitted_at":"2011-10-28T15:33:57Z","abstract_excerpt":"For any irreducible non-degenerate variety $X\\subset \\mathbb{P}^r$, we give a criterion for the $(k,s)$-identifiability of $X$. If $k\\leq s-1 <r$, then the $(k,s)$-identifiability holds for $X$ if and only if the $s$-identifiability holds for the Segre product $Seg(\\mathbb{P}^k\\times X)$. Moreover, if the $s$-th secant variety of $X$ is not defective and it does not fill the ambient space, then we can produce a family of pairs $(k,s)$ for which the $(k,s)$-identifiability holds for $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6367","kind":"arxiv","version":3},"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"}