Wild automorphisms of compact complex spaces of lower dimensions
Algebraic Geometry
2023-09-20 v2 Dynamical Systems
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 K\"ahler threefolds or fourfolds, and generalise the results of Oguiso--Zhang from the projective case to the K\"ahler case.
Keywords
Cite
@article{arxiv.2211.12245,
title = {Wild automorphisms of compact complex spaces of lower dimensions},
author = {Jia Jia and Long Wang},
journal= {arXiv preprint arXiv:2211.12245},
year = {2023}
}
Comments
Minor revision. Final version. arXiv admin note: text overlap with arXiv:2002.04437 by other authors