Germes de feuilletages pr\'esentables du plan complexe
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.
Keywords
Cite
@article{arxiv.1303.2866,
title = {Germes de feuilletages pr\'esentables du plan complexe},
author = {Loïc Teyssier},
journal= {arXiv preprint arXiv:1303.2866},
year = {2013}
}