Jordan property for groups of bimeromorphic automorphisms of compact Kähler threefolds

Abstract

Let X be a non-uniruled compact Kähler 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 Kähler space admitting a quasi-minimal model.

Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps

“…The main ideas of the proof are, however, already present in J. Xu's work (see e. g. the proof of [Xu18, Proposition 2.12]). Combining these ideas with some technical results from our paper [Gol21], we prove the same result for groups of bimeromorphic selfmaps of compact Kähler spaces of dimension 3.…”

“…Section 3 is devoted to the proof of our main theorem. First, in subsection 3.1 we use techniques from our previous paper [Gol21] to generalize Theorem 1.4 to pseudoautomorphisms of compact Kähler spaces with rational singularities (see Theorem 3.5). Then, in subsection 3.2 we prove the main theorem for non-uniruled projective varieties (Theorem 3.10), following the ideas from [Xu18, Section 2].…”