Automorphisms of rational surfaces with positive entropy

TL;DR

This paper constructs new examples of automorphisms with positive entropy on rational surfaces and discusses parameter counting in families of birational maps and rational surfaces.

Contribution

It introduces novel automorphisms of rational surfaces with positive entropy and provides methods for parameter counting in related families.

Findings

New automorphisms of rational surfaces with positive entropy

Parameter counting techniques for birational maps

Framework for constructing and analyzing rational surface automorphisms

Abstract

A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite mysterious and have been recently the object of intensive studies. In this paper, we construct several new examples of automorphisms of rational surfaces with positive topological entropy. We also explain how to define and to count parameters in families of birational maps of the complex projective plane and in families of rational surfaces.