Title: Generic singularities of holomorphic foliations by curves on $\mathbb{P}^n$ Show Chinese title

Title: 复曲线叶层的全纯叶层的通用奇点在$\mathbb{P}^n$

Abstract: Let $\mathcal{F}_d(\mathbb{P}^n)$ be the space of all singular holomorphic foliations by curves on $\mathbb{P}^n$ ($n \geq 2$) with degree $d \geq 1.$ We show that there is subset $\mathcal{S}_d(\mathbb{P}^n)$ of $\mathcal{F}_d(\mathbb{P}^n)$ with full Lebesgue measure with the following properties: 1. for every $\mathcal{F} \in \mathcal{S}_d(\mathbb{P}^n),$ all singular points of $\mathcal{F}$ are linearizable hyperbolic. 2. If, moreover, $d \geq 2,$ then every $\mathcal{F}$ does not possess any invariant algebraic curve. Show Chinese abstract

Abstract: 设$\mathcal{F}_d(\mathbb{P}^n)$为$\mathbb{P}^n$($n \geq 2$) 上所有次数为$d \geq 1.$的奇异解析曲线叶状结构的空间。我们证明存在一个子集$\mathcal{S}_d(\mathbb{P}^n)$属于$\mathcal{F}_d(\mathbb{P}^n)$，其勒贝格测度为全测度，具有以下性质： 1. 对于每个$\mathcal{F} \in \mathcal{S}_d(\mathbb{P}^n),$，$\mathcal{F}$的所有奇点都是可线性化的双曲点。 2. 如果此外，$d \geq 2,$，则每个$\mathcal{F}$都不具有任何不变代数曲线。