{"paper":{"title":"Symmetric tensor rank with a tangent vector: a generic uniqueness theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Edoardo Ballico","submitted_at":"2011-01-26T15:48:28Z","abstract_excerpt":"Let $X_{m,d}\\subset \\mathbb {P}^N$, $N:= \\binom{m+d}{m}-1$, be the order $d$ Veronese embedding of $\\mathbb {P}^m$. Let $\\tau (X_{m,d})\\subset \\mathbb {P}^N$, be the tangent developable of $X_{m,d}$. For each integer $t \\ge 2$ let $\\tau (X_{m,d},t)\\subseteq \\mathbb {P}^N$, be the joint of $\\tau (X_{m,d})$ and $t-2$ copies of $X_{m,d}$. Here we prove that if $m\\ge 2$, $d\\ge 7$ and $t \\le 1 + \\lfloor \\binom{m+d-2}{m}/(m+1)\\rfloor$, then for a general $P\\in \\tau (X_{m,d},t)$ there are uniquely determined $P_1,...,P_{t-2}\\in X_{m,d}$ and a unique tangent vector $\\nu$ of $X_{m,d}$ such that $P$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5090","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"}