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

Bonatti, C.; Langevin, R.; Moussu, R.

Publ. Math., Inst. Hautes Étud. Sci. 75, 123-134 (1992).

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.

Reviewer: A.Aeppli (Minneapolis)

MSC:

32S65

Singularities of holomorphic vector fields and foliations

Keywords:

holomorphic foliations

References:

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