Related papers: Conjugacy classes of linear actions in the plane C…
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.
In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the real projective plane.
The aim of this paper is to give a finer geometric description of the algebraic varieties parametrizing conjugacy classes of nonsolvable subgroups in the plane Cremona group.
This work presents the conjugacy classes of finite abelian subgroups of the Cremona group of the plane. Using a well-known theory, this problem amounts to the study of automorphism groups of some Del Pezzo surfaces and conic bundles. We…
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 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 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…
We classify birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which…
We classify, up to conjugacy, the finite (constant) subgroups G of adjoint absolutely simple algebraic groups of type $A_1$ over an arbitrary field $k$ of characteristic not 2.
We classify all finite subgroups of the plane Cremona group which have a fixed point. In other words, we determine all rational surfaces X with an action of a finite group G such that X is equivariantly birational to a surface which has a…
We prove that, except for a few cases, stable linearizability of finite subgroups of the plane Cremona group implies linearizability.
We study finite non-linearizable subgroups of the plane Cremona group which potentially could be stably linearizable.
This note presents the study of the conjugacy classes of elements of some given finite order n in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if n is even, n=3 or n=5, and that…
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 short note deals with the conjugacy classes of monomial birational maps in the $n$-dimensional Cremona group, $n\geq 2$.
We give a simple set of generators and relations for the Cremona group of the plane. Namely, we show that the Cremona group is the amalgamated product of the de Jonqui\`eres group with the group of automorphisms of the plane, divided by one…
Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…
We discuss the concept of Cremona contractible plane curves, with an historical account on the development of this subject. We then classify Cremona contractible unions of d > 11 lines in the plane.
An additive action on an irreducible algebraic variety $X$ is an effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the vector group $\mathbb{G}_a^n$. Any two additive actions on $X$ are conjugate by a birational…
We classify, up to conjugacy, the subgroups of the Cremona group isomorphic to (Z/p)^r, where p is prime and r is maximal.