On The Log Sarkisov Program For Foliations On Projective 3-Folds

TL;DR

This paper proves the Sarkisov Program for certain foliations on projective threefolds and explores a weaker form of birational super-rigidity between foliated Mori fiber spaces.

Contribution

It establishes the Sarkisov Program for co-rank one foliations with specific singularities on normal projective threefolds and introduces a weaker birational super-rigidity result.

Findings

Proved Sarkisov Program for co-rank one foliations on threefolds.

Established a weaker birational super-rigidity between foliated Mori fiber spaces.

Abstract

In this article, we prove the Sarkisov Program for co-rank one foliations with suitable singularities on normal projective threefolds. We also exibit a weaker version of birational super-rigidity between two foliated Mori fiber spaces with rank one foliations on normal projective threefolds.