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

@inproceedings{Loginov2022JordanPF, title={Jordan property for groups of bimeromorphic self-maps of complex manifolds with large Kodaira dimension}, author={Konstantin Loginov}, year={2022} }

. We prove that the image of the pluricanonical representation of a group of bimero- morphic 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.

## References

SHOWING 1-10 OF 18 REFERENCES

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

- Mathematics
- 2021

. 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…

### Finite groups of bimeromorphic selfmaps of non-uniruled K\"ahler threefolds

- Mathematics
- 2021

. We prove the Jordan property for groups of bimeromorphic selfmaps of three-dimensional compact K¨ahler varieties of non-negative Kodaira dimension and positive irregularity.

### Boundedness for finite subgroups of linear algebraic groups

- Mathematics
- 2020

We show the boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots of 1. Also, we provide explicit bounds for orders of finite…

### Resolution of singularities of analytic spaces

- Mathematics
- 2009

Building upon work of Villamayor Bierstone-Milman and our recent paper we give a proof of the canonical Hironaka principalization and desingularization of analytic spaces. Though the inductive scheme…

### Jordan property and automorphism groups of normal compact Kähler varieties

- Mathematics
- 2017

It has been recently shown by Meng and Zhang that the full automorphism group Aut(X) is a Jordan group for all projective varieties in arbitrary dimensions. The aim of this paper is to show that the…