53 citations · 60 across the 9 of their papers we have counts for
17 papers
Holomorphic foliations of degree four on the complex projective space
Arturo Fernández-Pérez, Vângellis Sagnori Maia
In this paper, we study holomorphic foliations of degree four on complex projective space , where , with a special focus on obtaining a structural theorem fo…
On Briançon-Skoda theorem for foliations
Arturo Fernández-Pérez, Evelia R. García Barroso, Nancy Saravia-Molina
We generalize Mattei's result relative to the Briançon-Skoda theorem for foliations to the family of foliations of the second type. We use this generalization to establish relation…
Chow's theorem for real analytic Levi-flat hypersurfaces
Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas
In this article we provide a version of Chow's theorem for real analytic Levi-flat hypersurfaces in the complex projective space , . More specifically, we…
On real-analytic Levi-flat hypersurfaces and holomorphic webs
Ayane Adelina Da Silva, Arturo Fernández-Pérez
We investigate holomorphic webs tangent to real-analytic Levi-flat hypersurfaces on compact complex surfaces. Under certain conditions, we prove that a holomorphic web tangent to a…
On Milnor and Tjurina numbers of foliations
Arturo Fernández-Pérez, Evelia R. García Barroso, Nancy Saravia-Molina
We study the relationship between the Milnor and Tjurina numbers of a singular foliation , in the complex plane, with respect to a balanced divisor of separatrices $\m…
On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance
Arturo Fernández-Pérez, Gilcione Nonato Costa, Rudy Rosas
We define the Milnor number -- as the intersection number of two holomorphic sections -- of a one-dimensional holomorphic foliation with respect to a compact connecte…
Pull-back of singular Levi-flat hypersurfaces
Andrés Beltrán, Arturo Fernández-Pérez, Hernán Neciosup
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-…
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…
Lehmann-Suwa residues of codimension one holomorphic foliations and applications
Arturo Fernández-Pérez, Jimmy Támara
Let be a singular codimension one holomorphic foliation on a compact complex manifold of dimension at least three such that its singular set has codimension at le…
Brunella-Khanedani-Suwa variational residues for invariant currents
Mauricio Corrêa, Arturo Fernández-Pérez, Marcio G. Soares
In this work we prove a Brunella-Khanedani-Suwa variational type residue theorem for currents invariant by holomorphic foliations. As a consequence, we give conditions for the leav…
On foliations by curves with singularities of positive dimension
Arturo Fernández-Pérez, Gilcione Nonato Costa
We present enumerative results for holomorphic foliations by curves on , , with singularities of positive dimension. Some of the results presented improve pr…
Residue-type indices and holomorphic foliations
Arturo Fernández-Pérez, Rogério Mol
We investigate residue-type indices for germs of holomorphic foliations in the plane and characterize second type foliations - those not containing tangent saddle-nodes in the redu…
Higher codimensional foliations and Kupka singularities
Maurício Corrêa, Omegar Calvo-Andrade, Arturo Fernández-Pérez
We consider holomorphic foliations of dimension and codimension in the projective space , with a compact connected component of the Kupka set. We prove…
On the dynamics of foliations in tangent to Levi-flat hypersurfaces
Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas
Let be a codimension one holomorphic foliation in , , leaving invariant a real-analytic Levi-flat hypersurface with regular part . T…
Absolutely -convex domains and holomorphic foliations on homogeneous manifolds
Mauricio Corrêa, Arturo Fernández-Pérez
We consider a holomorphic foliation of codimension on a homogeneous compact Kähler manifold of dimension . Assuming that the singular set $Sing(\ma…
On Levi-flat hypersurfaces tangent to holomorphic webs
Arturo Fernández-Pérez
We investigate germs of real analytic Levi-flat hypersurfaces tangent to germs of codimension one holomorphic webs. We introduce the notion of first integrals for local webs. In pa…
Quantum process reconstruction based on mutually unbiased basis
A. Fernández-Pérez, A. B. Klimov, C. Saavedra
We study a quantum process reconstruction based on the use of mutually unbiased projectors (MUB-projectors) as input states for a D-dimensional quantum system, with D being a power…