Let νd : Pr → PN, denote the degree d Veronese embedding of Pr. For any P ∈ PN, the symmetric tensor rank sr(P) is the minimal cardinality of a set S ⊂ νd(Pr) spanning P. Let S(P) be the set of all A ⊂ Pr such that νd(A) computes sr(P). Here we classify all P ∈ Pn such that sr(P) < 3d/2 and sr(P) is computed by at least two subsets of νd(Pr). For such tensors P ∈ PN, we prove that S(P) has no isolated points.
Ballico, E., Chiantini, L. (2013). Sets computing the symmetric tensor rank. MEDITERRANEAN JOURNAL OF MATHEMATICS, 10(2), 643-654 [10.1007/s00009-012-0214-4].
Sets computing the symmetric tensor rank
Chiantini L.
2013-01-01
Abstract
Let νd : Pr → PN, denote the degree d Veronese embedding of Pr. For any P ∈ PN, the symmetric tensor rank sr(P) is the minimal cardinality of a set S ⊂ νd(Pr) spanning P. Let S(P) be the set of all A ⊂ Pr such that νd(A) computes sr(P). Here we classify all P ∈ Pn such that sr(P) < 3d/2 and sr(P) is computed by at least two subsets of νd(Pr). For such tensors P ∈ PN, we prove that S(P) has no isolated points.
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https://hdl.handle.net/11365/44524
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