Bronowski’s conjecture and the identifiability of projective varieties

Let X ⊂ Phn+h-1 be an irreducible and nondegenerate variety of dimension n. Bronowski's conjecture predicts that X is h-identifiable if and only if the general h-1/-tangential projection τX h-1 W X -→ Pn is birational. In this paper we provide counterexamples to this conjecture. Building on the ideas that led to the counterexamples we manage to prove an amended version of the Bronowski's conjecture for a wide class of varieties and to reduce the identifiability problem for projective varieties to their secant defectiveness.