From non-defectivity to identifiability

A point $p$ in a projective space is $h$-identifiable via variety $X$ if there unique way to write as linear combination of $h$ points $X$. Identifiability important both algebraic geometry and applications. In this paper we propose an entirely new approach study identifiability, connecting it the notion secant defect for any smooth variety. are able improve known bounds on identifiability produce statements. particular, give optimal some Segre Segre–Veronese varieties provide first statements Grassmann varieties.