Automorphism groups of positive entropy on minimal projective varieties

TL;DR

This paper characterizes the structure of minimal projective varieties with automorphisms of positive entropy and provides bounds on their dynamical degrees, extending to higher dimensions.

Contribution

It generalizes the understanding of automorphism groups with positive entropy on minimal varieties and establishes effective bounds for their dynamical degrees.

Findings

Structural description of minimal projective threefolds with such automorphisms

Extension of results to higher-dimensional smooth minimal pairs

Effective lower bounds for the first dynamical degree in boundary cases

Abstract

We determine the geometric structure of a minimal projective threefold having two `independent and commutative' automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X, G). As a consequence, we give an effective lower bound for the first dynamical degree of these automorphisms of X fitting the `boundary case'.