The Sarkisov program for Mori fibred Calabi-Yau pairs

TL;DR

This paper extends the Sarkisov program to volume-preserving birational maps of Mori fibred Calabi-Yau pairs in all dimensions, generalizing previous results on 2D tori.

Contribution

It introduces a new version of the Sarkisov program applicable to higher-dimensional Calabi-Yau pairs, broadening the scope of birational geometry techniques.

Findings

Established a Sarkisov program for Mori fibred Calabi-Yau pairs in all dimensions.

Generalized the 2D torus volume-preserving map factorization to higher dimensions.

Provided a framework for analyzing birational maps preserving volume forms.

Abstract

We prove a version of the Sarkisov program for volume preserving birational maps of Mori fibred Calabi-Yau pairs valid in all dimensions. Our theorem generalises the theorem of Usnich and Blanc on factorisations of birational maps of the 2-dimensional torus that preserve the canonical volume form.