Distinguished Line Bundles for Complex Surface Automorphisms

TL;DR

This paper links the dynamical behaviors of complex surface automorphisms, such as entropy and periodic curves, to their actions on line bundles, providing a cohomological perspective on their measures of maximal entropy.

Contribution

It establishes a connection between dynamical properties and line bundle actions, offering new insights into the structure of automorphisms on complex surfaces.

Findings

Dynamical properties correspond to line bundle pull-back actions.

Cohomological methods describe measures of maximal entropy.

Positive entropy automorphisms have specific line bundle characteristics.

Abstract

We equate dynamical properties (e.g., positive entropy, existence of a periodic curve) of complex projective surface automorphisms with properties of the pull-back actions of such automorphisms on line bundles. We use the properties of the cohomological actions to describe the measures of maximal entropy for automorphisms with positive entropy.