A Minkowski-style Bound for the Orders of the Finite Subgroups of the Cremona Group of Rank 2 over an Arbitrary Field

2009 ◽  
Vol 9 (1) ◽  
pp. 183-198 ◽  
Author(s):  
J. P. Serre
Keyword(s):  
Arbitrary Field ◽  
Cremona Group ◽  
Finite Subgroups ◽  
Rank 2

scholarly journals Free Poisson fields and their automorphisms

2016 ◽  
Vol 15 (10) ◽  
pp. 1650196 ◽  
Author(s):  
Leonid Makar-Limanov ◽  
Ualbai Umirbaev
Keyword(s):  
Universal Enveloping Algebra ◽  
Arbitrary Field ◽  
Group Of Automorphisms ◽  
Cremona Group ◽  
Enveloping Algebra ◽  
Ideal Ring ◽  
Poisson Fields ◽  
Poisson Field

Let [Formula: see text] be an arbitrary field of characteristic [Formula: see text]. We prove that the group of automorphisms of a free Poisson field [Formula: see text] in two variables [Formula: see text] over [Formula: see text] is isomorphic to the Cremona group [Formula: see text]. We also prove that the universal enveloping algebra [Formula: see text] of a free Poisson field [Formula: see text] is a free ideal ring and give a characterization of the Poisson dependence of two elements of [Formula: see text] via universal derivatives.

scholarly journals Sur l'hyperbolicit\'e de graphes associ\'es au groupe de Cremona

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Anne Lonjou
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Closed Field ◽  
Cremona Group ◽  
Curve Graph ◽  
Gromov Hyperbolic ◽  
Rank 2

To reinforce the analogy between the mapping class group and the Cremona group of rank $2$ over an algebraic closed field, we look for a graph analoguous to the curve graph and such that the Cremona group acts on it non-trivially. A candidate is a graph introduced by D. Wright. However, we demonstrate that it is not Gromov-hyperbolic. This answers a question of A. Minasyan and D. Osin. Then, we construct two graphs associated to a Vorono\"i tesselation of the Cremona group introduced in a previous work of the autor. We show that one is quasi-isometric to the Wright graph. We prove that the second one is Gromov-hyperbolic. Comment: 29 pages, en Fran\c{c}ais

scholarly journals Finite Subgroups of the Plane Cremona Group

2009 ◽  
pp. 443-548 ◽  
Author(s):  
Igor V. Dolgachev ◽  
Vasily A. Iskovskikh
Keyword(s):  
Cremona Group ◽  
Finite Subgroups

scholarly journals On stable conjugacy of finite subgroups of the plane Cremona group, I

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Fedor Bogomolov ◽  
Yuri Prokhorov
Keyword(s):  
Prime Order ◽  
Cremona Group ◽  
Cyclic Groups ◽  
Group I ◽  
Finite Subgroups ◽  
Birational Invariant

AbstractWe discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We compute the stable birational invariant H 1(G, Pic(X)) for cyclic groups of prime order.

On 2-groups with finite subgroups of rank 2

2016 ◽  
Vol 57 (3) ◽  
pp. 532-537
Author(s):  
D. V. Lytkina ◽  
V. D. Mazurov
Keyword(s):  
Finite Subgroups ◽  
Rank 2
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