Identifiability holds for the k-secant variety σk(X) of an embedded variety X ⊂ Pr if a general q ∈ σk(X) is in the linear span of a unique subset of X with cardinality k. We consider here the case in which X is a Segre-Veronese embedding of a multiprojective space, i.e. q corresponds to a partially symmetric tensor and X-rank is the partially symmetric tensor rank. To improve by 1 the known results we exclude the case of codimension one contact loci and handle cases in which the irreducible components of the tangential k-contact locus are linear spaces.
Identifiability for the k-secant variety of the Segre-Veronese varieties / Ballico, Edoardo. - In: LINEAR & MULTILINEAR ALGEBRA. - ISSN 0308-1087. - STAMPA. - 70:21(2022), pp. 6441-6451. [10.1080/03081087.2021.1957077]
Identifiability for the k-secant variety of the Segre-Veronese varieties
Ballico, Edoardo
2022-01-01
Abstract
Identifiability holds for the k-secant variety σk(X) of an embedded variety X ⊂ Pr if a general q ∈ σk(X) is in the linear span of a unique subset of X with cardinality k. We consider here the case in which X is a Segre-Veronese embedding of a multiprojective space, i.e. q corresponds to a partially symmetric tensor and X-rank is the partially symmetric tensor rank. To improve by 1 the known results we exclude the case of codimension one contact loci and handle cases in which the irreducible components of the tangential k-contact locus are linear spaces.File | Dimensione | Formato | |
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