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