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

Abstract

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

Minor revision. Final version

References in corpus (1)

• Jordan property for automorphism groups of compact spaces in Fujiki's class $C$

Cited by in corpus (1)

• Wild automorphisms of compact complex spaces of lower dimensions