MMP for algebraically integrable foliations

TL;DR

This paper establishes a link between the termination of flips in algebraic geometry and the existence of minimal models for algebraically integrable foliations with specific singularities.

Contribution

It proves that flip termination in certain dimensions implies the existence of minimal models for algebraically integrable foliations with log canonical singularities.

Findings

Flip termination implies minimal model existence for foliations

Results hold over $Q$-factorial klt projective varieties

Applicable in dimension r for algebraically integrable foliations

Abstract

We show that termination of flips for $\mathbb Q$-factorial klt pairs in dimension $r$ implies existence of minimal models for algebraically integrable foliations of rank $r$ with log canonical singularities over a $\mathbb Q$-factorial klt projective variety.