New examples of holomorphic foliations without algebraic leaves
Henryk Żołądek (1998)
Studia Mathematica
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We present a series of polynomial planar vector fields without algebraic invariant curves in .
Displaying similar documents to “Vector fields, invariant varieties and linear systems”
New examples of holomorphic foliations without algebraic leaves
The polar curve of a foliation on
Rogério S. Mol (2010)
Annales de la faculté des sciences de Toulouse Mathématiques
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We study some properties of the polar curve associated to a singular holomorphic foliation on the complex projective plane . We prove that, for a generic center , the curve is irreducible and its singular points are exactly the singular points of with vanishing linear part. We also obtain upper bounds for the algebraic multiplicities of the singularities of and for its number of radial singularities.
On plane polynomial vector fields and the Poincaré problem.
El Kahoui, M'hammed (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Multiplicity of a foliation on projective spaces along an integral curve.
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.
Minimal models of foliated algebraic surfaces
Marco Brunella (1999)
Bulletin de la Société Mathématique de France
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Foliations in algebraic surfaces having a rational first integral.
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.
Holomorphic foliations by curves on with non-isolated singularities
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.