Remarks on bitrational relations of toric Mori fiber spaces

TL;DR

This paper explores the relationships between Mori fiber spaces obtained via the minimal model program on toric varieties, showing they are interconnected through elementary transforms.

Contribution

It demonstrates that any two Mori fiber spaces from the MMP on a toric variety are connected by finitely many elementary transforms, extending understanding of their structure.

Findings

Any two Mori fiber spaces from the MMP are connected by elementary transforms.

The MMP can be run for any divisor on a Q-factorial projective toric variety.

Connections between Mori fiber spaces are finitely many and explicit.

Abstract

We can run the MMP for any divisor on any $\mathbb{Q}$-factorial projective toric variety. We show that two Mori fiber spaces, which are outputs of the above MMP, are connected by finitely many elementary transforms.