Recent progress on the Minimal Model Program for foliations

TL;DR

This paper surveys recent advances in the birational geometry of foliations on complex varieties, emphasizing the Minimal Model Program and its recent developments.

Contribution

It provides a comprehensive overview of recent progress on the MMP for foliations, including singularities, adjunction, and flip existence.

Findings

Progress on the MMP for foliations on surfaces

Results on the existence of flips on threefolds

Advances in understanding singularities and adjunction for foliations

Abstract

We survey recent progress on the birational geometry of foliations on complex varieties. We focus on the MMP viewpoint: singularities, adjunction and applications to the MMP for foliations on surfaces and to the existence of flips on threefolds.