• Corpus ID: 252531800

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

. 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

. 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

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

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

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