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Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 07/2018, Volume 38, Issue 7, pp. 3223 - 3237
We study in this paper several properties concerning singularities of foliations in (C-3, 0) that are pull-back of dicritical foliations in (C-2, 0).... 
Holomorphic foliations, dicritical foliations | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | dicritical foliations | Holomorphic foliations | DESINGULARIZATION | SINGULAR FOLIATIONS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 05/2013, Volume 238, pp. 70 - 118
In this paper we address Fano foliations on complex projective varieties. These are foliations ℱ whose anti-canonical class −Kℱ is ample. We focus our... 
Holomorphic foliations and vector fields | Rationally connected varieties | BOGOMOLOV | MATHEMATICS | MODELS | FAMILIES | PROJECTIVE SPACES | VARIETIES | CLASSIFICATION | RATIONAL CURVES | MANIFOLDS | VECTOR BUNDLES | Algebraic Geometry | Mathematics
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 9/2018, Volume 213, Issue 3, pp. 1327 - 1380
This paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds. 
Mathematics, general | Mathematics | KAHLER-MANIFOLDS | MATHEMATICS | HOLOMORPHIC FOLIATIONS | SPACES | STABILITY | VARIETIES | VECTOR-BUNDLES | Algebraic Geometry
Journal Article
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, ISSN 1079-2724, 07/2019, Volume 25, Issue 3, pp. 491 - 516
We consider germs of holomorphic vector fields in (Cn,0), n 3, with non-isolated singularities. We assume that the set of singular points forms a submanifold... 
MATHEMATICS, APPLIED | Normal forms | Non-isolated singularities | Holomorphic vector fields | Foliations | AUTOMATION & CONTROL SYSTEMS | Monodromy | Microorganisms
Journal Article
Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 08/2017, Volume 37, Issue 5, pp. 1443 - 1479
In this paper we give complete analytic invariants for the set of germs of holomorphic foliations in (C-2,0) that become regular after a single blow-up. Some... 
MATHEMATICS | MATHEMATICS, APPLIED | GERMS | HOLOMORPHIC FOLIATIONS | SINGULARITIES | PLANE | C-2 | VECTOR-FIELDS | MODULI | Singularities | Mathematical analysis | Invariants | Classification | Complex Variables | Dynamical Systems | Mathematics
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2018, Volume 68, Issue 2, pp. 511 - 539
We study a special kind of local invariant sets of singular holomorphic foliations called nodal separators. We define notions of equisingularity and... 
Equisingularity | Topological equivalence | Holomorphic foliation | MATHEMATICS | topological equivalence | equisingularity
Journal Article
Advances in Mathematics, ISSN 0001-8708, 11/2017, Volume 320, pp. 1158 - 1184
In this work we prove a Baum–Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the... 
Residues | Holomorphic foliations | Characteristic classes | MATHEMATICS | Dynamical Systems | Mathematical Physics | Algebraic Topology | K-Theory and Homology | Operator Algebras | Algebraic Geometry | Mathematics | Differential Geometry
Journal Article
REVISTA MATEMATICA IBEROAMERICANA, ISSN 0213-2230, 2019, Volume 35, Issue 4, pp. 1153 - 1194
Let (X,F) be a foliated surface and G a finite group of automorphisms of X that preserves F. We investigate invariant loci for G and obtain upper bounds for... 
holomorphic foliations | MATHEMATICS | Automorphism
Journal Article
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 01/2019, Volume 371, Issue 2, pp. 949 - 969
We present a new list of irreducible components for the space of k-dimensional holomorphic foliations on P-n, n >= 3, k >= 2. They are associated to pull-back... 
MATHEMATICS | irreducible components | Holomorphic foliations | STABILITY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2014, Volume 416, Issue 2, pp. 683 - 697
We prove that any transversally holomorphic map between Kähler foliations is transversally harmonic with the minimum transversal fk-energy in its foliated... 
Transversally holomorphic field | Generalized Jacobi field | Transversally harmonic map | Transversally holomorphic map | MATHEMATICS | FIELDS | MATHEMATICS, APPLIED | HARMONIC MAPS | INFINITESIMAL AUTOMORPHISMS | RIEMANNIAN FOLIATIONS | MANIFOLDS
Journal Article
Expositiones Mathematicae, ISSN 0723-0869, 06/2019, Volume 37, Issue 2, pp. 145 - 164
In this survey paper, we take the viewpoint of polar invariants to the local and global study of non-dicritical holomorphic foliation in dimension two and... 
Polar curves | Invariant curves | Holomorphic foliation | Secondary | Primary | MATHEMATICS | HYPERSURFACE | HOLOMORPHIC FOLIATIONS | INDEX | CURVES
Journal Article
11/2010
This thesis is devoted to the study of foliations that come from dynamical systems. In the first part we study foliations of Stein manifolds locally given by... 
Henon maps | foliations | multidimensional complex analysis | holomorphic dynamics | 0405
Dissertation
The Journal of Geometric Analysis, ISSN 1050-6926, 4/2019, Volume 29, Issue 2, pp. 1407 - 1427
An irreducible real analytic subvariety H of real dimension $$2n +1$$ 2 n + 1 in a complex manifold M is a Levi-flat subset if its regular part carries a... 
Abstract Harmonic Analysis | Primary 32S65 | Fourier Analysis | Secondary 32V40 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Holomorphic foliations | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | CR-manifolds | Levi-flat varieties | MATHEMATICS | SINGULARITIES | HYPERSURFACES
Journal Article
Anais da Academia Brasileira de Ciencias, ISSN 0001-3765, 10/2017, Volume 89, Issue 4, pp. 2563 - 2579
In this paper we study topological and analytical conditions on the orbits of a germ of diffeomorphism in the complex plane in order to obtain periodicity. In... 
Closed orbits | Complex germs of diffeomorphims | Integrability of vector fields | Singular holomorphic foliations | closed orbits | HOLOMORPHIC FOLIATIONS | SINGULARITIES | MULTIDISCIPLINARY SCIENCES | singular holomorphic foliations | integrability of vector fields
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2019, Volume 113, Issue 4, pp. 4017 - 4030
The purpose of this work is to obtain the degree of the exceptional component of the space of holomorphic foliations of degree two and codimension one in... 
14N99 | Degree | Theoretical, Mathematical and Computational Physics | Exceptional component | 57R30 | Mathematics, general | Mathematics | Applications of Mathematics | Foliations | Bott’s formula | SPACE | MATHEMATICS | HOLOMORPHIC FOLIATIONS | Bott's formula | Automorphisms | Parameters
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 11/2019, Volume 25, Issue 3, pp. 619 - 635
In this article, for holomorphic foliations of codimension one at $$(\mathbb {C}^3,0)$$ ( C 3 , 0 ) , we define the family of second type foliations. This is... 
Invariant varieties | 32S65 | Equidesingularization | 37F75 | Mathematics, general | Holomorphic foliations | Mathematics
Journal Article
COLLOQUIUM MATHEMATICUM, ISSN 0010-1354, 2019, Volume 156, Issue 2, pp. 229 - 242
Journal Article
Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, 06/2017, Volume 48, Issue 2, pp. 219 - 235
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00574-016-0003-y We give... 
Baum–Bott Theorem | Holomorphic foliations | Weighted projective space | Poincaré problem
Journal Article
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, ISSN 0012-9593, 11/2018, Volume 51, Issue 6, pp. 1457 - 1506
This article studies codimension one foliations on projective manifolds having a compact leaf (free of singularities). It explores the interplay between Ueda... 
MATHEMATICS
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 03/2017, Volume 28, Issue 3, p. 1750019
We consider holomorphic foliations of dimension k > 1 and codimension ≥ 1 in the projective space ℙ n , with a compact connected component of the Kupka set. We... 
holomorphic foliations | Kupka singular set | MATHEMATICS | NORMAL BUNDLE | COMPONENT
Journal Article
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