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Identifiability holds for the  k -secant variety  σk( X ) of an embedded varietyif a general  q  ∈  σk( 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 Γk ⊂  X  has dimension 0. Under certain assumptions onfor some specific  x &gt; k , we get. Here we give some conditions which exclude the case Γxa hypersurface for some  x &gt; k  and getand 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 ofcorresponds to partially symmetric tensors.

Identifiability for the k -secant variety of the Segre-Veronese varieties