Publications by Christian Lucius Urech

Characterization of affine surfaces with a torus action by their automorphism groups

In this paper we prove that if two normal affine surfaces S and S' have isomorphic automophism groups, then every connected algebraic group acting regularly and faithfully on S acts also regularly and faithfully on S'. Moreover, if S is non-toric, we show ...

2023

Cremona Groups Over Finite Fields, Neretin Groups, and Non-Positively Curved Cube Complexes

Christian Lucius Urech

We show that plane Cremona groups over finite fields embed as dense subgroups into Neretin groups, that is, groups of almost automorphisms of rooted trees. We also show that if the finite base field has even characteristic and contains at least four elemen ...

2023

Subgroups of elliptic elements of the Cremona group

Christian Lucius Urech

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the struc ...

2021

Continuous automorphisms of Cremona groups

Christian Lucius Urech

We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show that a similar ...

2021

Simple groups of birational transformations in dimension two

Christian Lucius Urech

We classify simple groups that act by birational transformations on compact complex Kahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective surface over an arbitrar ...

2020