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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
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References:

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