Related papers: p-elementary subgroups of the Cremona group

For the subgroups of the Cremona group $\mathrm{Cr}_3(\mathbb C)$ having the form $(\boldsymbol{\mu}_p)^s$, where $p$ is prime, we obtain an upper bound for $s$. Our bound is sharp if $p\ge 17$.

We give the classification of elements - respectively cyclic subgroups - of finite order of the Cremona group, up to conjugation. Natural parametrisations of conjugacy classes, related to fixed curves of positive genus, are provided.

We give a complete classification of maximal algebraic subgroups of the Cremona group of the plane and provide algebraic varieties that parametrize the conjugacy classes. ----- Nous donnons une classification compl\`ete des sous-groupes…

This paper contains a new proof of the classification of elements of prime order in the Cremona group Bir(P^2), up to conjugation. In addition, we give explicit geometric constructions of these Cremona transformations, and provide a…

We obtain a sharp bound for p-elementary subgroups in the plane Cremona group over an arbitrary perfect field.

We describe the endomorphisms of the Cremona group and obtain that the Cremona group is hopfian.

For each prime p, we exhibit pairs of p-groups all of whose integral cohomology groups are isomorphic. The method used involves very little calculation. The groups are exhibited as kernels of homomorphisms from a compact Lie group G to…

We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in a maximal algebraic subgroup of the plane Cremona group. We classify the maximal groups, and their subgroups of rational points, up…

We give an explicit set of generators for various natural subgroups of the real Cremona group Bir_R(P^2). This completes and unifies former results by several authors.

We find an upper bound for the number of groups of order $n$ up to isomorphism in the variety $G = A_pA_qA_r$, where $p$, $q$ and $r$ are distinct primes. We also find a bound on the orders and on the number of conjugacy classes of…

We give the classification of the maximal infinite algebraic subgroups of the real Cremona group of the plane up to conjugacy and present a parametrisation space of each conjugacy class. Moreover, we show that the real plane Cremona group…

Two elements in a group $G$ are said to $z$-equivalent or to be in the same $z$-class if their centralizers are conjugate in $G$. In \cite{kkj}, it was proved that a non-abelian $p$-group $G$ can have at most $\frac{p^k-1}{p-1} +1$ number…

We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.

We complete the classical and modern work on the classification of conjugacy classes of finite subgroups of the group of birational transformations of the complex projective plane.

We classify regular generically free actions of finite groups on the projective plane, up to conjugation in the Cremona group.

This article shows that the Cremona group is compactly presentable. To prove this we show that it is a generalised amalgamated product of three of its algebraic subgroups (automorphisms of the plane and Hirzebruch surfaces) divided by one…

We classify elementary abelian 2 subgroups of compact simple Lie groups of adjoint type. This finishes the classification of elementary abelian $p$ subgroups of compact (or linear algebraic) simple groups of adjoint type.

In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the real projective plane.

Recall that a $p$-group of order $p^ {n} >p^ {3} $ is of maximal class, if its nilpotency class is $n-1$. In this paper, we study the $p$-groups of maximal class. Furthermore, we introduce a subgroup of a $p$-group of maximal class called…

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…