{"paper":{"title":"A new class of non-identifiable skew symmetric tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Davide Vanzo","submitted_at":"2016-06-13T22:22:21Z","abstract_excerpt":"We prove that the generic element of the fifth secant variety $\\sigma_5(Gr(\\mathbb{P}^2,\\mathbb{P}^9)) \\subset \\mathbb{P}(\\bigwedge^3 \\mathbb{C}^{10})$ of the Grassmannian of planes of $\\mathbb{P}^9$ has exactly two decompositions as a sum of five projective classes of decomposable skew-symmetric tensors. {We show that this, {together with $Gr(\\mathbb{P}^3, \\mathbb{P}^8)$, is the only non-identifiable case} among the non-defective secant varieties $\\sigma_s(Gr(\\mathbb{P}^k, \\mathbb{P}^n))$ for any $n<14$. In the same range for $n$, we classify all the weakly defective and all tangentially weak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04158","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"}