Jordan property for groups of bimeromorphic automorphisms of compact K\"ahler threefolds

TL;DR

This paper proves that the group of bimeromorphic automorphisms of certain compact K"ahler threefolds is Jordan, extending the property to spaces with a quasi-minimal model, which has implications for understanding their symmetry groups.

Contribution

The paper establishes the Jordan property for bimeromorphic automorphism groups of compact K"ahler threefolds and spaces with quasi-minimal models, broadening previous results in complex geometry.

Findings

Group of bimeromorphic automorphisms is Jordan for these spaces

Extends Jordan property to spaces with quasi-minimal models

Provides structural insights into automorphism groups of K"ahler threefolds

Abstract

Let $X$ be a non-uniruled compact K\"ahler space of dimension 3. We show that the group of bimeromorphic automorphisms of $X$ is Jordan. More generally, the same result holds for any compact K\"ahler space admitting a quasi-minimal model.