On tangential weak defectiveness and identifiability of projective varieties

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 linea...

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Bibliographic Details
Published inarXiv.org
Main Authors Ageu Barbosa Freire, Casarotti, Alex, Massarenti, Alex
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.01.2022
Subjects
Vector spaces
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Summary: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.
ISSN:2331-8422