论文标题
布朗诺夫斯基的猜想和投影品种的可识别性
Bronowski's conjecture and the identifiability of projective varieties
论文作者
论文摘要
令$ x \ subset \ mathbb {p}^{hn+h-1} $是不可减少和非分类的尺寸$ n $。 Bronowski的猜想预测$ x $是$ h $ - 可识别的，并且仅当常规$（H-1）$ - 切向投影$τ_{h-1}^x：x \ dashrightArrow \ dashrightArrow \ mathbb {p}^n $是Birational。在本文中，我们为此猜想提供反例。以导致反例的想法为基础，我们设法证明了布罗诺夫斯基（Bronowski）对各种品种的猜想的修订版，并将投射性品种的可识别性问题减少到其脱离损失。
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.
