Flop between algebraically integrable foliations on potentially klt varieties

TL;DR

This paper establishes that minimal models of lc algebraically integrable foliated triples on potentially klt varieties are connected via flops, extending the understanding of their birational geometry and minimal model connections.

Contribution

It proves the existence of flop sequences connecting minimal models of algebraically integrable foliated triples on potentially klt varieties, and discusses implications for non-integrable foliations.

Findings

Minimal models are connected by flops on potentially klt varieties.

Flop sequences exist between minimal models of algebraically integrable foliated triples.

Connections between minimal models are established under certain MMP assumptions.

Abstract

We prove that for any two minimal models of an lc algebraically integrable foliated triple on potentially klt varieties, there exist small birational models that are connected by a sequence of flops. In particular, any two minimal models of lc algebraically integrable foliated triples on $\mathbb Q$-factorial klt varieties are connected by a sequence of flops. We also discuss the connection between minimal models for possibly non-algebraically integrable foliations on threefolds, assuming the minimal model program for generalized foliated quadruples.