Related papers: Finite subgroups of the plane Cremona group

An equivariant stable birational invariant of an action of a finite group on a smooth projective variety is the first cohomology group of the Picard module. Bogomolov-Prokhorov and Shinder computed this for actions of cyclic groups on…

The Cremona group of birational transformations of $\mathbb{P}^2_\mathbb{C}$ acts on the space $\mathbb{F}(2)$ of holomorphic foliations on the complex projective plane. Since this action is not compatible with the natural graduation of…

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.

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

This work gives a classification of imprimitive irreducible finite subgroups of the orthogonal group O(7) plus the number of conjugate classes for each group.

One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of…

We prove that groups definable in o-minimal structures have Cartan subgroups, and only finitely many conjugacy classes of such subgroups. We also delineate with precision how these subgroups cover the ambient group, in general very largely…

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.

We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic Q. Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the plane…

We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of maximal finite subgroups of the…

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…

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

We show that the alternating groups $\mathfrak{A}_5$ and $\mathfrak{A}_6$ are the only finite simple non-abelian subgroups of the group of birational selfmaps of the real three-dimensional projective space.

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 the paper we complete the classification of Carter subgroups in finite almost simple groups. In particular, we prove that Carter subgroups of every finite almost simple group are conjugate. Togeather with previous results by author and…

In this paper we study birational Kleinian groups, i.e.\ groups of birational transformations of complex projective varieties acting in a free, properly discontinuous and cocompact way on an open set of the variety with respect to the usual…

We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

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

We give a presentation of the plane Cremona group over an algebraically closed field with respect to the generators given by the Theorem of Noether and Castelnuovo. This presentation is particularly simple and can be used for explicit…