Displaying similar documents to “Minimal models of foliated algebraic surfaces”

On dicritical foliations and Halphen pencils

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.

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 ℙ 3 with non-isolated singularities

Gilcione Nonato Costa (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let ℱ be a holomorphic foliation by curves on ℙ 3 . We treat the case where the set Sing ( ℱ ) 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 ℱ , the multiplicity of ℱ along the curves and the degree and genus of the curves.

Vector fields and foliations on compact surfaces of class VII 0

Georges Dloussky, Karl Oeljeklaus (1999)

Annales de l'institut Fourier

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It is well-known that minimal compact complex surfaces with b 2 > 0 containing are in the class VII 0 of Kodaira. In fact, there are no other known examples. In this paper we prove that all surfaces with global spherical shells admit a singular holomorphic foliation. The existence of a numerically anticanonical divisor is a necessary condition for the existence of a global holomorphic vector field. Conversely, given the existence of a numerically anticanonical divisor, surfaces with a global...