Bronowski's conjecture and the identifiability of projective varieties
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917566777131008 |
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| author | Massarenti, Alex Mella, Massimiliano |
| author_facet | Massarenti, Alex Mella, Massimiliano |
| contents | 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 $τ_{h-1}^X:X\dashrightarrow\mathbb{P}^n$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13524 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bronowski's conjecture and the identifiability of projective varieties Massarenti, Alex Mella, Massimiliano Algebraic Geometry Primary 14N07, Secondary 14N05, 14N15, 14M15, 15A69, 15A75 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 $τ_{h-1}^X:X\dashrightarrow\mathbb{P}^n$ 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. |
| title | Bronowski's conjecture and the identifiability of projective varieties |
| topic | Algebraic Geometry Primary 14N07, Secondary 14N05, 14N15, 14M15, 15A69, 15A75 |
| url | https://arxiv.org/abs/2210.13524 |