On Fano foliations

In this paper we address Fano foliations on complex projective varieties. These are foliations ℱ whose anti-canonical class −Kℱ is ample. We focus our attention on a special class of Fano foliations, namely del Pezzo foliations on complex projective manifolds. We show that these foliations are algebraically integrable, with one exceptional case when the ambient space is Pn. We also provide a classification of del Pezzo foliations with mild singularities.