Automorphism groups of compact complex surfaces: T-Jordan property, Tits alternative and solvability

TL;DR

This paper investigates the structure of automorphism groups of compact complex surfaces, establishing their torsion subgroups are virtually nilpotent and analyzing their Tits alternative and solvability properties.

Contribution

It provides new insights into the algebraic structure of automorphism groups of compact complex surfaces, including nilpotency and solvability aspects.

Findings

Torsion subgroup of Aut(X) is virtually nilpotent

Aut(X) satisfies the Tits alternative

Virtually solvable subgroups have bounded derived length

Abstract

Let $X$ be a (smooth) compact complex surface. We show that the torsion subgroup of the biholomorphic automorphism group $\operatorname{Aut}(X)$ is virtually nilpotent. Moreover, we study the Tits alternative of $\operatorname{Aut}(X)$ and virtual derived length of virtually solvable subgroups of $\operatorname{Aut}(X)$.