In this paper we consider various notions of positivity for distributions on complex projective manifolds. We start by analyzing distributions having big slope with respect to curve classes, obtaining characterizations of generic projective space bundles in terms of movable curve classes. We then apply this result to investigate algebraicity of leaves of foliations, providing a lower bound for the algebraic rank of a foliation in terms of invariants measuring positivity. We classify foliations attaining this bound, and describe those whose algebraic rank slightly exceeds this bound.

中文翻译：

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一般射影空间丛的表征和叶理的代数性

在本文中，我们考虑了复杂射影流形上分布的各种正性概念。我们首先分析相对于曲线类具有大斜率的分布，根据可移动曲线类获得通用射影空间丛的特征。然后我们应用这个结果来研究叶的叶子的代数性，根据测量积极性的不变量为叶的代数等级提供下限。我们对达到这个界限的叶进行分类，并描述那些代数等级略超过这个界限的叶。