On the MMP for rank one foliations on threefolds

Abstract

We prove existence of flips for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. This, in particular, provides a proof of the existence of a minimal model for a rank one foliation on a threefold for a wider range of singularities, after McQuillan.

arXiv comment57 pages. Exposition improved based on referee's suggestions. Final version. Forum of Mathematics, Pi (to appear)