Pisot units, Salem numbers and higher dimensional projective manifolds with primitive automorphisms of positive entropy

TL;DR

This paper demonstrates the existence of higher-dimensional complex manifolds, including abelian, rational, and Calabi-Yau varieties, with primitive automorphisms exhibiting positive entropy, advancing understanding of dynamical systems in algebraic geometry.

Contribution

It constructs explicit examples of higher-dimensional manifolds with primitive automorphisms of positive entropy, extending known results to new classes of complex varieties.

Findings

Existence of abelian varieties with primitive automorphisms of degree >1

Existence of Calabi-Yau manifolds with primitive automorphisms of positive entropy

Construction of rational manifolds with primitive automorphisms in even dimensions

Abstract

We show that, in any dimension greater than one, there are an abelian variety, a smooth rational variety and a Calabi-Yau manifold, with primitive birational automorphisms of first dynamical degree $>1$. We also show that there are smooth complex projective Calabi-Yau manifolds and smooth rational manifolds, of any even dimension, with primitive biregular automorphisms of positive topological entropy.