Jordan property for groups of bimeromorphic self-maps of complex manifolds with large Kodaira dimension

TL;DR

This paper proves that groups of bimeromorphic automorphisms of complex manifolds with high Kodaira dimension have the Jordan property, by showing their pluricanonical representations have bounded finite subgroups.

Contribution

It establishes the Jordan property for bimeromorphic automorphism groups of complex manifolds with large Kodaira dimension, extending previous results to higher dimensions.

Findings

The image of the pluricanonical representation has bounded finite subgroups.

Groups of bimeromorphic automorphisms with Kodaira dimension ≥ n-2 satisfy the Jordan property.

The result applies to complex manifolds of dimension n with high Kodaira dimension.

Abstract

We prove that the image of the pluricanonical representation of a group of bimeromorphic automorphisms of a complex manifold has bounded finite subgroups. As a consequence, we show that the group of bimeromorphic automorphisms of an $n$-dimensional complex manifold whose Kodaira dimension is at least $n-2$, satisfies the Jordan property.