Continuous Families of Rational Surface Automorphisms with Positive Entropy

TL;DR

This paper constructs multi-parameter families of rational surface automorphisms with positive entropy, providing explicit examples and analyzing their automorphism groups and inequivalence conditions.

Contribution

It introduces a method to generate k-parameter families of rational surface automorphisms with positive entropy, expanding the understanding of their structure and classification.

Findings

Constructed k-parameter families of automorphisms for any k

Determined automorphism groups in specific cases

Established criteria for surface inequivalence

Abstract

We construct k-parameter families of rational surface automorphisms for any k. These are automorphisms of surfaces X, which are constructed from iterated blowups over the projective plane. In certain cases: we are able to determine the exact automorphism group of X, as well as when two of the surfaces X are inequivalent.