15 citations · 22 across the 12 of their papers we have counts for
19 papers
Characterizing Varieties Using Birational Transformations
Nathan Chen, Louis Esser, Andriy Regeta +2
Suppose is an irreducible complex variety. We show that when is ruled, the group of birational transformations , as a group, determines up to birational transfo…
Asymptotically rigid mapping class groups III: Presentations and isomorphisms
Anthony Genevois, Anne Lonjou, Christian Urech
This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we…
Representations of finite subgroups of Cremona groups
Alexander Duncan, Bailey Heath, Christian Urech
The Cremona group of rank n over a field k is the group of birational automorphisms of the n-dimensional projective space over the field k. We study the minimal dimension such that…
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…
On a Theorem by Lin and Shinder through the Lens of Median Geometry
Anthony Genevois, Anne Lonjou, Christian Urech
Recently, Lin and Shinder constructed non-trivial homomorphisms from Cremona groups of rank >2 to \mathbb{Z} using motivic techniques. In this short note we propose an alternative…
Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded
Anne Lonjou, Piotr Przytycki, Christian Urech
We prove that any finitely generated subgroup of the plane Cremona group consisting only of algebraic elements is of bounded degree. This follows from a more general result on `dec…
Cremona groups over finite fields, Neretin groups, and non-positively curved cube complexes
Anthony Genevois, Anne Lonjou, Christian Urech
We show that plane Cremona groups over finite fields embed as dense subgroups into Neretin groups, i.e. groups of almost automorphisms of rooted trees. We also show that if the fin…
Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature
Anthony Genevois, Anne Lonjou, Christian Urech
In this article, we introduce a new family of groups, called Chambord groups and constructed from braided strand diagrams associated to specific semigroup presentations. It include…
Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
Anthony Genevois, Anne Lonjou, Christian Urech
This article is dedicated to the study of asymptotically rigid mapping class groups of infinitely-punctured surfaces obtained by thickening planar trees. Such groups include the br…
Actions of Cremona groups on CAT(0) cube complexes
Anne Lonjou, Christian Urech
For each d we construct CAT(0) cube complexes on which Cremona groups rank d act by isometries. From these actions we deduce new and old group theoretical and dynamical results abo…
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…
On the characterization of Danielewski surfaces by their automorphism group
Alvaro Liendo, Andriy Regeta, Christian Urech
In this note we show that if the automorphism group of a normal affine surface is isomorphic to the automorphism group of a Danielewski surface, then is isomorphic to a Dan…
Characterization of affine surfaces with a torus action by their automorphism groups
Alvaro Liendo, Andriy Regeta, Christian Urech
In this paper we prove that if two normal affine surfaces and have isomorphic automorphism groups, then every connected algebraic group acting regularly and faithfully on…
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…
Remarks on the degree growth of birational transformations
Christian Urech
We look at sequences of positive integers that can be realized as degree sequences of iterates of rational dominant maps of smooth projective varieties over arbitrary fields. New c…
On homomorphisms between Cremona groups
Christian Urech
We look at algebraic embeddings of the Cremona group in variables to the group of birational transformations of an algebraic variety . First we study geom…