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On dicritical foliations and Halphen pencils

Luís Gustavo MendesPaulo Sad — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.

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