Pseudo-Automorphisms of positive entropy on the blowups of products of projective spaces

TL;DR

This paper constructs pseudo-automorphisms with positive entropy on blowups of projective spaces and their products, providing new examples of complex dynamics in higher-dimensional rational varieties.

Contribution

It introduces a concise method to construct pseudo-automorphisms with positive entropy on blowups of projective spaces and their products, including the first such examples in higher dimensions.

Findings

Constructed pseudo-automorphisms with d_1(f_n) > 1 for all n > 1

Provided the first examples of non-product type pseudo-automorphisms with positive entropy in higher dimensions

Demonstrated the existence of complex dynamics on rational varieties of dimension greater than two

Abstract

We use a concise method to construct pseudo-automorphisms f_n of the first dynamical degree d_1(f_n) > 1 on the blowups of the projective n-space for all n > 1 and more generally on the blowups of products of projective spaces. These f_n, for n = 3 have positive entropy, and for n > 3 seem to be the first examples of pseudo-automorphisms with d_1(f_n) > 1 (and of non-product type) on rational varieties of higher dimensions.