{"paper":{"title":"Typical and Admissible ranks over fields","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":"2016-04-08T13:04:17Z","abstract_excerpt":"Let $X(\\RR)$ be a geometrically connected variety defined over $\\RR$ and such that the set of all its (also complex) points $X(\\CC)$ is non-degenerate.\n  We introduce the notion of \\emph{admissible rank} of a point $P$ with respect to $X$ to be the minimal cardinality of a set of points of $X(\\CC)$ such that $P\\in \\langle S \\rangle$ that is stable under conjugation.\n  Any set evincing the admissible rank can be equipped with a \\emph{label} keeping track of the number of its complex and real points. We show that in the case of generic identifiability there is an open dense euclidean subset of p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02342","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"}