7 papers · 1 filter
Separatrices for real analytic vector fields in the plane
Eduardo Cabrera, Rogério Mol
Let be a germ of real analytic vector field at with an algebracally isolated singularity. We say that is a topological generalized curve if there are…
Holomorphic vector fields tangent to foliations in dimension three
Danúbia Junca, Rogério Mol
This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we…
On singular real analytic Levi-flat foliations
Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas
A singular real analytic foliation of real codimension one on an -dimensional complex manifold is Levi-flat if each of its leaves is foliated by immersed compl…
Real Analytic Vector Fields with First Integral and Separatrices
Rogério Mol, Fernando Sanz Sánchez
We prove that a germ of analytic vector field at that possesses a non-constant analytic first integral has a real formal separatrix. We provide an example which…
Second type foliations of codimension one
Gilberto Cuzzuol, Rogério Mol
In this article, for holomorphic foliations of codimension one at , we define the family of second type foliations. This is formed by foliations having, in the…
Holomorphic foliations tangent to Levi-flat subsets
Jane Bretas, Arturo Fernández-Pérez, Rogério Mol
We study Segre varieties associated to Levi-flat subsets in complex manifolds and apply them to establish local and global results on the integration of tangent holomorphic foliati…