Related papers: The Cremona group and its subgroups

The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other…

In this note we describe the embeddings of the Heisenberg group into the Cremona group.

We classify, up to conjugacy, the subgroups of the Cremona group isomorphic to (Z/p)^r, where p is prime and r is maximal.

This article studies algebraic elements of the Cremona group. In particular, we show that the set of all these elements is a countable union of closed subsets but it is not closed.

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.

This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.

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

This expository article builds on lecture notes from a minicourse entitled "Cremona groups and CAT(0) cube complexes" and given by the author as part of the 2023 Riverside Workshop on Geometric Group Theory. It presents recent constructions…

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…

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

We study finite non-linearizable subgroups of the plane Cremona group which potentially could be stably linearizable.

We study embeddings of symmetric groups to the space Cremona group.

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 is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…

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.

This paper is concerned with suitable generalizations of a plane de Jonqui\`eres map to higher dimensional space $\mathbb{P}^n$ with $n\geq 3$. For each given point of $\mathbb{P}^n$ there is a subgroup of the entire Cremona group of…

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).

The Cremona group is connected in any dimension and, endowed with its topology, it is simple in dimension 2. ----- Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension 2.

We study the algebraic structure of the $n$-dimensional Cremona group and show that it is not an algebraic group of infinite dimension (ind-group) if $n\ge 2$. We describe the obstruction to this, which is of a topological nature. By…