On tangential weak defectiveness and identifiability of projective varieties

Abstract

A point $p\in {\mathbb{P}}^N$ of a projective space is $h$-identifiable, with respect to a variety $X\subset {\mathbb{P}}^N$, 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 $X\subset {\mathbb{P}}^N$, and we apply these results to Segre-Veronese varieties.

17 pages