arXiv subjects

Hernán Neciosup

Publications and source records attributed to Hernán Neciosup.

5 recordsLinked to original sources

arXiv2021

Pull-back of singular Levi-flat hypersurfaces

We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat hypersurface in a complex projective surface under a rational map or to be the pull-back of a real algebraic curve under a meromorphic function. In particular, we give an application to the case of a singular real analytic Levi-flat hypersurface. Our results improve previous ones due to Lebl and Bretas -- Fernández-Pérez -- Mol.

math.CV↗

arXiv2017

Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in $\mathbb{P}^2$.

math.CV↗

arXiv2017

Dicritical nilpotent holomorphic foliations

We study in this paper several properties concerning singularities of foliations in $(\mathbb{C}^3,\mathbf{0})$ that are pull-back of dicritical foliations in $(\mathbb{C}^2,\mathbf{0})$. Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in $(\mathbb{C}^2,\mathbf{0})$, the adaptations are not straightforward.

math.DS↗

arXiv2016

Analytic classification of a class of cuspidal foliations in $({\mathbb C}^3,0)$

In this article we study the analytic classification of certain types of quasi-homogeneous cuspidal holomorphic foliations in $(\CC^3,{\bf 0})$ via the essential holonomy defined over one of the components of the exceptional divisor that appears in the reduction of the singularities of the foliation.

math.DS↗

arXiv2013

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. We will also give a sufficient condition, in the quasi-homogeneous, three-dimensional case, for these foliations to be of generalized surface type.

math.DS↗