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Foliations in $$\mathbb{C} P(n)$$: About hyperbolic holonomy for minimal exceptional sets. (Feuilletages de $$\mathbf C\mathbf P(n)$$: De l’holonomie hyperbolique pour les minimaux exceptionnels.) (French) Zbl 0782.32023
Does there exist a holomorphic foliation $${\mathcal F}$$ of codimension $$l$$ in $$\mathbb{C} P(n)$$ with a minimal exceptional set, i.e. with a leaf $$L$$ whose closure $$\overline L$$ does not contain any singular point of $${\mathcal F}$$? The answer is not known. However, the authors show: given a holomorphic foliation $${\mathcal F}$$ of codimension $$l$$ in $$\mathbb{C} P(n)$$ with a leaf $$L$$ such that $$\overline L$$ is disjoint from the singular set of $${\mathcal F}$$, there exists a loop in a leaf contained in $$\overline L$$ with contracting hyperbolic holonomy.

##### MSC:
 32S65 Singularities of holomorphic vector fields and foliations
##### Keywords:
holomorphic foliations
Full Text:
##### References:
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