Germes de feuilletages présentables du plan complexe

Loïc Teyssier

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arXiv · 1303.2866

Germes de feuilletages présentables du plan complexe

Loïc Teyssier

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Abstract

Let F be a germ of a singular foliation of the complex plane. Assuming that F is a generalized curve D. Marin and J.-F. Mattei proved the incompressibility of the foliation in a neighborhood from which a finite set of analytic curves is removed. We show in the present work that this hypothesis cannot be eluded by building examples of foliations, reduced after one blow-up, for which the property does not hold. Even if we manage to prove that the individual saddle-node foliation is incompressible, their leaves not retracting tangentially on the boundary of the domain of definition forbids a generalization of Marin--Mattei's construction. We finally characterize those foliations for which the construction of Marin--Mattei's monodromy can be carried out.

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Loïc Teyssier. 2013-11-26. Germes de feuilletages présentables du plan complexe. https://arxiv.org/abs/1303.2866

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