On codimension one foliations with prescribed cuspidal separatrix
In this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. As an application, we will explain how this form could be used in order to study the analytic classification of the singularities via the projective holonomy, in the generalized surface case. We will also give an application to the analytic classification of singularities, and a sufficient condition, in the quasi-homogeneous, three-dimensional case, for these foliations to be of generalized surface type.
Autor(es):Fernández-Sánchez, Percy;
Mozo-Fernández, Jorge;
Neciosup, Hernán
Año: 2014
Título de la revista: Journal of Differential Equations
Volumen: 256
Página inicial - Página final: 1702-1717
ISSN: 0022-0396
Url: http://www.sciencedirect.com/science/article/pii/S0022039613004968