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pro vyhledávání: '"Urech, Christian"'
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 ruled. Additionally, we prove that any Borel subgroup of Bir(X) has deriv
Externí odkaz:
http://arxiv.org/abs/2409.07864
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 families satisfy a Chevalley type result and a certain fibre-dimension
Externí odkaz:
http://arxiv.org/abs/2409.06475
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 perspective from median geometry on their theorem.
Comment: 6 pag
Comment: 6 pag
Externí odkaz:
http://arxiv.org/abs/2312.05197
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 `decent' actions on infinite direct sums. We apply our results to describe
Externí odkaz:
http://arxiv.org/abs/2307.01334
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 finite base field has even characteristic and contains at least 4 element
Externí odkaz:
http://arxiv.org/abs/2110.14605
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 includes the asymptotically rigid mapping class groups previously studied by
Externí odkaz:
http://arxiv.org/abs/2110.06721
Publikováno v:
Geom. Topol. 26 (2022) 1385-1434
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 braided Ptolemy-Thompson groups $T^\sharp,T^\ast$ introduced by Funar an
Externí odkaz:
http://arxiv.org/abs/2010.07225
Autor:
Lonjou, Anne, Urech, Christian
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 about Cremona groups. In particular, we study the dynamical behaviour of
Externí odkaz:
http://arxiv.org/abs/2001.00783
Autor:
Urech, Christian, Zimmermann, Susanna
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 si
Externí odkaz:
http://arxiv.org/abs/1909.11050
Publikováno v:
Transformation Groups (2020)
In this note we show that if the automorphism group of a normal affine surface $S$ is isomorphic to the automorphism group of a Danielewski surface, then $S$ is isomorphic to a Danielewski surface.
Comment: 5 pages. Minor changes as suggested by
Comment: 5 pages. Minor changes as suggested by
Externí odkaz:
http://arxiv.org/abs/1905.00423