Wild automorphisms of compact complex spaces of lower dimensions

Abstract

An automorphism of a compact complex space is called wild in the sense of Reichstein--Rogalski--Zhang if there is no non-trivial proper invariant analytic subset. We show that a compact complex surface admitting a wild automorphism must be a complex torus or an Inoue surface of certain type, and this wild automorphism has zero entropy. As a by-product of our argument, we obtain new results about the automorphism groups of Inoue surfaces. We also study wild automorphisms of compact Kähler threefolds or fourfolds, and generalise the results of Oguiso--Zhang from the projective case to the Kähler case.

Minor revision. Final version. arXiv admin note: text overlap with arXiv:2002.04437 by other authors

References in corpus (4)

• Automorphisms of parabolic Inoue surfaces
• Wild automorphisms of projective varieties, the maps which have no invariant proper subsets
• Equivariant Kähler model for Fujiki's class
• Automorphism groups of compact complex surfaces: T-Jordan property, Tits alternative and solvability