On the MMP for rank one foliations on threefolds

TL;DR

This paper proves the existence of flips for rank one foliated pairs on threefolds, advancing the minimal model program in the context of foliations with broader singularity classes.

Contribution

It establishes the existence of flips for log canonical foliated pairs of rank one on Q-factorial projective klt threefolds, extending previous results.

Findings

Existence of flips for rank one foliated pairs on threefolds.

Proof of minimal model existence for rank one foliations.

Broader singularity classes covered after McQuillan.

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.