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arXiv · 2210.13524

Bronowski's conjecture and the identifiability of projective varieties

Alex Massarenti·Massimiliano Mella
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Abstract

Let $X\subset\mathbb{P}^{hn+h-1}$ 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 $\tau_{h-1}^X:X\dashrightarrow\mathbb{P}^n$ 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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Alex Massarenti, Massimiliano Mella. 2022-10-24. Bronowski's conjecture and the identifiability of projective varieties. https://arxiv.org/abs/2210.13524

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