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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.
We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.
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