On tangential weak defectiveness and identifiability of projective varieties

Ageu Barbosa Freire, Alex Casarotti, Alex Massarenti

Published 2020-02-23Version 1

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 and flag varieties.