Regularizations of positive entropy pseudo-automorphisms

TL;DR

This paper investigates conditions under which positive entropy birational automorphisms of threefolds are non-regularizable, applying these criteria to a specific example in projective three-space and analyzing its structural properties.

Contribution

It provides new criteria for non-regularizability of positive entropy automorphisms and applies these to a notable example in algebraic geometry.

Findings

The automorphism in the example is non-regularizable for general parameters.

The automorphism does not preserve a fibration over a surface.

Criteria for non-regularizability are established and applied.

Abstract

We study positive entropy birational automorphisms of threefolds. We identify some conditions which imply that such an automorphism is non-regularizable. We show that this criterion applies in the example of a positive entropy birational automorphism of $\mathbb{P}^3$ constructed by J. Blanc, thus showing that for a general choice of parameters it is non-regularizable. Additionally, we establish a criterion which proves that the automorphism in this example does not preserve a structure of a fibration over a surface.