On Dicritical Foliations and Halphen Pencils

Paulo Sad | Mendes, Luís Gustavo

Keywords: Dicritical singularities | Halphen pencils | elliptic fibrations.

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.

Anexos:

• enfim.dvi