Holomorphic foliations in having an invariant algebraic curve
Dominique Cerveau, Alcides Lins Neto (1991)
Annales de l'institut Fourier
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We give estimations for the degree of separatrices of algebraic foliations in .
Dominique Cerveau, Alcides Lins Neto (1991)
Annales de l'institut Fourier
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We give estimations for the degree of separatrices of algebraic foliations in .
Paulo Sad (1999)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Julio García (1993)
Revista Matemática de la Universidad Complutense de Madrid
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We compute the global multiplicity of a 1-dimensional foliation along an integral curve in projective spaces. We give a bound in the way of Poincaré problem for a complete intersection curves. In the projective plane, this bound give us a bound of the degree of non irreducible integral curves in function of the degree of the foliation.
Gilcione Nonato Costa (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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Let be a holomorphic foliation by curves on . We treat the case where the set consists of disjoint regular curves and some isolated points outside of them. In this situation, using Baum-Bott’s formula and Porteuos’theorem, we determine the number of isolated singularities, counted with multiplicities, in terms of the degree of , the multiplicity of along the curves and the degree and genus of the curves.
Alexis García Zamora (1997)
Publicacions Matemàtiques
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Given a foliation in an algebraic surface having a rational first integral a genus formula for the general solution is obtained. In the case S = P some new counter-examples to the classic formulation of the Poincaré problem are presented. If S is a rational surface and has singularities of type (1, 1) or (1,-1) we prove that the general solution is a non-singular curve.
E. Ballico (1999)
Rendiconti del Seminario Matematico della Università di Padova
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Luís Gustavo Mendes, Paulo Sad (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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The aim of this article is to provide information on the number and on the geometrical position of singularities of holomorphic foliations of the projective plane. As an application it is shown that certain foliations are in fact Halphen pencils of elliptic curves. The results follow from Miyaoka’s semipositivity theorem, combined with recent developments on the birational geometry of foliations.