Bronowski's conjecture and the identifiability of projective varieties

2022/10/24 by Alex Massarenti, Massimiliano Mella, Massarenti, Alex +1 · 4 citations
Mathematics · #14M15 #14N15 #15A69 #15A75 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Primary 14N07 #Secondary 14N05 #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2210.13524

openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X⊂ℙ^hn+h-1 be an irreducible and non-degenerate variety of dimension n. The Bronowski's conjecture predicts that X is h-identifiable if and only if the general (h-1)-tangential projection τ_h-1^X:X\dashrightarrowℙⁿ 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.

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