8 papers
Group Theoretical Characterizations of Rationality
Andriy Regeta, Christian Urech, Immanuel van Santen
Let X be an irreducible variety and Bir(X) its group of birational transformations. We show that the group structure of Bir(X) determines whether X is rational and whether X is rul…
The Structure of Algebraic Families of Birational Transformations
Andriy Regeta, Christian Urech, Immanuel van Santen
We give a description of the algebraic families of birational transformations of an algebraic variety X. As an application, we show that the morphisms to Bir(X) given by algebraic…
Continuous automorphisms of Cremona groups
Christian Urech, Susanna Zimmermann
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…
Simple groups of birational transformations in dimension two
Christian Urech
We classify simple groups that act by birational transformations on compact complex Kähler surfaces. Moreover, we show that every finitely generated simple group that acts non-triv…
Subgroups of elliptic elements of the Cremona group
Christian 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 e…
A new presentation of the plane Cremona group
Christian Urech, Susanna Zimmermann
We give a presentation of the plane Cremona group over an algebraically closed field with respect to the generators given by the Theorem of Noether and Castelnuovo. This presentati…