Identifiability for the k-secant variety of the Segre-Veronese varieties. Issue 21 (20th December 2022)

• Record Type: Journal Article
• Authors: Ballico, E.
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 21(2022)
• Page Start: 6441
• Page End: 6451
• Publication Date: 2022-12-20
• Subjects: Secant variety -- Segre-Veronese variety -- symmetric tensor rank -- identifiability -- contact locus -- multiprojective space; 14N05 -- 15A69; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1957077
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: Identifiability holds for the k -secant variety σ k ( X ) of an embedded variety X ⊂ P r if a general q ∈ σ k ( X ) is in the linear span of a unique subset of X with cardinality k . Identifiability is true if the general tangential k -contact locus Γ k ⊂ X has dimension 0. Under certain assumptions on dim ⁡ σ x ( X ) for some specific x > k, we get dim ⁡ Γ k = 0 . Here we give some conditions which exclude the case Γ x a hypersurface for some x > k and get dim ⁡ Γ k = 0 and hence identifiability for the k -secant variety. As an example we consider the case of Segre-Veronese embeddings of multiprojective spaces, in which the elements of P r corresponds to partially symmetric tensors.