On tangential weak defectiveness and identifiability of projective varieties

A point p is an element of P-N of a projective space is h-identifiable, with respect to a variety X subset of P-N, if it can be written as linear combination of h elements of X in a unique way. Identifiability is implied by conditions on the contact locus in X of general linear spaces called non weak defectiveness and non tangential weak defectiveness. We give conditions ensuring non tangential weak defectiveness of an irreducible and non-degenerated projective variety X subset of P-N, and we apply these results to Segre-Veronese varieties.