Bounded automorphism groups of compact complex surfaces

TL;DR

This paper classifies certain compact complex surfaces based on the boundedness of their automorphism groups' finite subgroups and extends results to Kähler manifolds with non-negative Kodaira dimension.

Contribution

It provides a classification of compact complex surfaces with bounded automorphism groups and generalizes boundedness results to broader classes of Kähler manifolds.

Findings

Classification of surfaces with bounded automorphism groups

Boundedness of stabilizers in automorphism groups of Kähler manifolds

Extension of boundedness results to non-negative Kodaira dimension

Abstract

We classify compact complex surfaces whose groups of bimeromorphic selfmaps have bounded finite subgroups. We also prove that the stabilizer of a point in the automorphism group of a compact complex surface of zero Kodaira dimension, as well as the stabilizer of a point in the automorphism group of an arbitrary compact Kaehler manifold of non-negative Kodaira dimension, always has bounded finite subgroups.