Germes de feuilletages présentables du plan complexe

Loïc Teyssier (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Systèmes dynamiques [math.DS]

Loïc Teyssier. Germes de feuilletages présentables du plan complexe. Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society, 2015, 46 (2), pp.275-329. ⟨10.1007/s00574-015-0093-y⟩. ⟨hal-00799548v3⟩