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Displaying similar documents to “Vector fields and foliations on compact surfaces of class VII 0 ”

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.

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.

Classification of singular germs of mappings and deformations of compact surfaces of class VII₀

Georges Dloussky, Franz Kohler (1998)

Annales Polonici Mathematici

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We classify generic germs of contracting holomorphic mappings which factorize through blowing-ups, under the relation of conjugation by invertible germs of mappings. As for Hopf surfaces, this is the key to the study of compact complex surfaces with b 1 = 1 and b ₂ > 0 which contain a global spherical shell. We study automorphisms and deformations and we show that these generic surfaces are endowed with a holomorphic foliation which is unique and stable under any deformation.