... Geometric Theory of Foliations. By Cesar Camacho and Alcides Lins Neto. The American Mathematical Monthly: Vol. 96, No. ...
Tópico(s): Computational Geometry and Mesh Generation
1989 - Taylor & Francis | American Mathematical Monthly
Produção Nacional
Revisado por pares
Tópico(s): Analytic Number Theory Research
1980 - Springer Science+Business Media | Inventiones mathematicae
Produção Nacional
Revisado por pares
César Camacho, Alcides Lins Neto,
Tópico(s): Algebraic Geometry and Number Theory
1982 - Springer Nature | Publications mathématiques de l IHÉS
César Camacho, Alcides Lins Neto, Paulo Sad,
The integrals of a holomorphic vector field Z defined in an open subset °U of C" are complex curves parametrized locally as the solutions of the differential equation They define a complex one-dimensional foliation J^z of °U with singularities at the zeros of Z.The purpose of this paper is to exhibit several topological invariants of these foliations near a singular point.Let Θ n be the ring of germs of holomorphic functions defined in some neighborhood of 0 G C w and let /(Z^ ,Z M ) be the ideal generated ...
Tópico(s): Homotopy and Cohomology in Algebraic Topology
1984 - Lehigh University | Journal of Differential Geometry
Tópico(s): Meromorphic and Entire Functions
1987 - Lehigh University | Journal of Differential Geometry
Produção Nacional
Revisado por pares
Tópico(s): Nonlinear Waves and Solitons
1988 - Springer Nature | Lecture notes in mathematics
Produção Nacional
Revisado por pares
César Camacho, Alcides Lins Neto, Paulo Sad,
Tópico(s): Advanced Differential Equations and Dynamical Systems
1988 - Springer Nature | Publications mathématiques de l IHÉS
Produção Nacional
Revisado por pares
Xavier Gómez-Mont, Alcides Lins-Neto,
Tópico(s): Mathematical Dynamics and Fractals
1991 - Elsevier BV | Topology
Dominique Cerveau, Alcides Lins Neto,
Nous estimons le degré des séparatrices d'un feuilletage algébrique de CP(2) en fonction du degré du feuilletage.
Tópico(s): Geometric and Algebraic Topology
1991 - Association of the Annals of the Fourier Institute | Annales de l’institut Fourier
César Camacho, Alcides Lins Neto, Paulo Sad,
Tópico(s): Computational Geometry and Mesh Generation
1992 - Princeton University | Annals of Mathematics
Produção Nacional
Revisado por pares
In 1891, Poincaré started a series of three papers in which he tried to answer the following question (cf. [21–23]): "Is it possible to decide if an algebraic differential equation in two variables is algebraically integrable?" (in the sense that it has a rational first integral). More or less at the same time P. Painlevé asked the following question: "Is it possible to recognize the genus of the general solution of an algebraic differential equation in two variables which has a rational first integral?". ...
Tópico(s): Nonlinear Waves and Solitons
2002 - Société Mathématique de France | Annales Scientifiques de l École Normale Supérieure
Produção Nacional
Tópico(s): Geometry and complex manifolds
1994 - Springer Science+Business Media | Boletim da Sociedade Brasileira de Matemática
Produção Nacional
Revisado por pares
Dominique Cerveau, Alcides Lins Neto, Frank Loray, Jorge Vitório Pereira, Frédéric Touzet,
Let F be a codimension one singular holomorphic foliation on a compact complex manifold M. Assume that there exists a meromorphic vector field X on M generically transversal to F. Then, we prove that F is the meromorphic pull-back of an algebraic foliation on an algebraic manifold N, or F is transversely projective outside a compact hypersurface, improving our previous work (see version 1). Such a vector field insures the existence of a global meromorphic Godbillon-Vey sequence for the foliation ...
Tópico(s): Algebraic Geometry and Number Theory
2007 - Independent University of Moscow | Moscow Mathematical Journal
Produção Nacional
Revisado por pares
Dominique Cerveau, Alcides Lins Neto,
In this paper we study codimension one holomorphic foliations leaving invariant real analytic hypersurfaces. In particular, we prove that a germ of real analytic Levi-flat hypersurface with sufficiently ``small" singular set is given by the zeroes of the imaginary part of a holomorphic function.
Tópico(s): Advanced Differential Equations and Dynamical Systems
2011 - Johns Hopkins University Press | American Journal of Mathematics
Produção Nacional
Revisado por pares
Michel Berthier, Dominique Cerveau, Alcides Lins Neto,
Tópico(s): History and Theory of Mathematics
1996 - Elsevier BV | Journal of Differential Equations
Alcides Lins Neto, Márcio G. Soares,
In this article we consider the problem of extending the result of J.P.Jouanolou on the density of singular holomorphic foliations on CP(2) without algebraic solutions to the case of foliations by curves of CP(n).
Tópico(s): Numerical methods for differential equations
1996 - Lehigh University | Journal of Differential Geometry
Dominique Cerveau, Alcides Lins Neto,
In this paper we will prove that the space of holomorphic fo- liations of codimension 1 and degree 2 in CP(n), n > 3, has six irreducible components.
Tópico(s): Meromorphic and Entire Functions
1996 - Princeton University | Annals of Mathematics
Produção Nacional
Revisado por pares
Omegar Calvo-Andrade, Dominique Cerveau, Luis Giraldo, Alcides Lins Neto,
In this paper, we give the explicit construction of certain components of the space of holomorphic foliations of codimension one, in complex projective spaces. These components are associated to some algebraic representations of the affine Lie algebra $\mathfrak{aff}(\mathbb{C})$ . Some of them, the so-called exceptional or Klein – Lie components, are rigid in the sense that all generic foliations in the component are equivalent (Example 1). In particular, we obtain rigid foliations of all degrees. Some ...
Tópico(s): Advanced Differential Geometry Research
2004 - Cambridge University Press | Ergodic Theory and Dynamical Systems
Produção Nacional
Dominique Cerveau, Alcides Lins Neto,
Tópico(s): Advanced Differential Equations and Dynamical Systems
2000 - Springer Science+Business Media | Boletim da Sociedade Brasileira de Matemática
Produção Nacional
Tópico(s): Mathematical Dynamics and Fractals
2000 - Springer Science+Business Media | Boletim da Sociedade Brasileira de Matemática
Produção Nacional
Revisado por pares
Dominique Cerveau, Alcides Lins Neto,
Let F be a codimension-one foliation on P n : for each point p ∈ P n we define J (F, p) as the order of the first non-zero jet j k p (ω) of a holomorphic 1form ω defining F at p.The singular set of F is sing(F) = { p ∈ P n | J (F, p) ≥ 1}.We prove (main Theorem 1.2) that a foliation F satisfying J (F, p) ≤ 1 for all p ∈ P n has a non-constant rational first integral.Using this fact we are able to prove that any foliation of degree-three on P n , with n ≥ 3, is either the pull-back of a foliation on P 2 , or has a transverse ...
Tópico(s): Point processes and geometric inequalities
2013 - | ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
Alcides Lins Neto, Paulo Sad, Bruno Scárdua,
Let us denote by X(n) the space of degree n G N foliations of the complex projective plane CP(2) which leave invariant the line at infinity.We prove that for each n > 2 there exists an open dense subset Rig(n) C X{n) such that any topologically trivial analytic deformation {J^t}t^ of an element FQ £ Rig(n), with J~t € ^{n}, for all t € D, is analytically trivial.This is an improvement of a remarkable result of Ilyashenko.Other generalizations of these results are given as well as a description of the class ...
Tópico(s): Geometric and Algebraic Topology
1998 - Société Mathématique de France | Bulletin de la Société mathématique de France
In this paper we prove that holomorphic codimension one singular foliations on ℂℙ n ,n≥3 have no non trivial minimal sets. We prove also that for n≥3, there is no real analytic Levi flat hypersurface in ℂℙ n .
Tópico(s): Advanced Differential Equations and Dynamical Systems
1999 - Association of the Annals of the Fourier Institute | Annales de l’institut Fourier
Dominique Cerveau, Alcides Lins Neto,
Tópico(s): Homotopy and Cohomology in Algebraic Topology
1984 - Cellule MathDoc/CEDRAM | Annales de la faculté des sciences de Toulouse Mathématiques
Produção Nacional
Revisado por pares
Tópico(s): Polynomial and algebraic computation
2015 - Springer Science+Business Media | Bulletin of the Brazilian Mathematical Society New Series
Produção Nacional
Revisado por pares
Dominique Cerveau, Alcides Lins Neto,
This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Conversely we show the existence of codimension two foliations which are not contained in any codimension one foliation. We study problems related to the singular locus and we classify homogeneous foliations of small degree.
Tópico(s): Algebraic Geometry and Number Theory
2019 - Lehigh University | Journal of Differential Geometry
Produção Nacional
Revisado por pares
Tópico(s): Advanced Differential Equations and Dynamical Systems
1983 - Springer Nature | Lecture notes in mathematics
Produção Nacional
Revisado por pares
Dominique Cerveau, Alcides Lins-Neto, Frank Loray, Jorge Vitório Pereira, Frédéric Touzet,
Let $M$ be a compact complex manifold equipped with $n=\dim(M)$ meromorphic vector fields that are linearly independent at a generic point. The main theorem is the following. If $M$ is not bimeromorphic to an algebraic manifold, then any codimension one complex foliation $\mathcal F$ with a codimension $\ge2$ singular set is the meromorphic pull-back of an algebraic foliation on a lower dimensional algebraic manifold, or $\mathcal F$ is transversely projective outside a proper analytic subset. The two ingredients ...
Tópico(s): Geometry and complex manifolds
2006 - European Mathematical Society | Commentarii Mathematici Helvetici
Produção Nacional
Revisado por pares
César Camacho, Alcides Lins Neto,
Tópico(s): Quantum chaos and dynamical systems
1977 - Springer Nature | Lecture notes in mathematics
Produção Nacional
Revisado por pares
Alcides Lins Neto, Jorge Vitório Pereira,
Our main result says that the generic rank of the Baum–Bott map for foliations of degree is not the pull-back of a foliation of smaller degree. In Appendix A we show that the monodromy of the singular set of the universal foliation with very ample cotangent bundle is the full symmetric group.
Tópico(s): Geometric and Algebraic Topology
2006 - Cambridge University Press | Compositio Mathematica