Symmetric Tensor Rank with a Tangent Vector: a Generic Uniqueness Theorem
نویسنده
چکیده
Let Xm,d ⊂ PN , N := `m+d m ́ −1, be the order d Veronese embedding of Pm. Let τ(Xm,d) ⊂ PN , be the tangent developable of Xm,d. For each integer t ≥ 2 let τ(Xm,d, t) ⊆ PN , be the joint of τ(Xm,d) and t− 2 copies of Xm,d. Here we prove that if m ≥ 2, d ≥ 7 and t ≤ 1 + b `m+d−2 m ́ /(m + 1)c, then for a general P ∈ τ(Xm,d, t) there are uniquely determined P1, . . . , Pt−2 ∈ Xm,d and a unique tangent vector ν of Xm,d such that P is in the linear span of ν ∪ {P1, . . . , Pt−2}, i.e. a degree d linear form f associated to P may be written as f = Ld−1 t−1Lt + t−2 X
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