Related papers: The Jordan constant for Cremona group of rank 2

In this paper we compute the Jordan constants of the Cremona group of rank two over all fields of characteristic zero.

We give explicit bounds for Jordan constants of groups of birational automorphisms of rationally connected threefolds over fields of zero characteristic, in particular, for Cremona groups of ranks 2 and 3.

In this paper we find the exact value of the Jordan constant for Cremona group of rank $2$ over all finite fields. During the proof we construct a cubic surface over $\mathbb{F}_2$ with a regular action of the group $\mathrm{S}_6$ which is…

We determine the Jordan constants of groups $\mathrm{GL}_2(K)$, $\mathrm{SL}_2(K)$, $\mathrm{PGL}_2(K)$ and $\mathrm{PGL}_3(K)$ for any given field $K$ of characteristic 0.

We show that the Cremona group of rank $2$ over a finite field is Jordan, and provide an upper bound for its Jordan constant which is sharp when the number of elements in the field is different from $2$, $4$, and $8$.

We study automorphism and birational automorphism groups of varieties over fields of positive characteristic from the point of view of Jordan and $p$-Jordan property. In particular, we show that the Cremona group of rank $2$ over a field of…

In this paper, we find the maximum values that the Jordan constant of the automorphism group of a smooth two-dimensional rational quadric over a field of characteristic zero can attain, depending on the arithmetic properties of a field.

We show that the Jordan constant for the volume-preserving plane Cremona group $\mathrm{Bir}(\mathbb P^2, \Delta)$ is $12$. We provide a Jordan bound of $144$ for the three-dimensional volume-preserving Cremona group $\mathrm{Bir}(\mathbb…

We bound the indices of normal abelian subgroups in finite groups contained in the Cremona group of rank 2 over a field of odd characteristic.

We compute the exact values of the Jordan constants of abelian surfaces over finite fields.

We compute and provide a detailed description on the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, we determine the Jordan constants of the multiplicative…

We show an analogue of Jordan's theorem for algebraic groups defined over a field $\mathbb k$ of arbitrary characteristic. As a consequence, a Jordan-type property holds for the automorphism group of any projective variety over $\mathbb k$.

The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of simple polarized abelian fourfolds over finite fields. As an application, we compute the Jordan constants of…

In this work, the automorphism group schemes of finite-dimensional simple Jordan pairs of types I and IV, and of some Jordan triple systems related to them, are determined. We assume $\mathrm{char}(\mathbb{F}) \neq 2$ for the base field…

Let $W$ be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that $W$ is birational to a product of a smooth projective variety $A$ and the projective line. We prove that if $A$ contains no rational…

We use a recent advance in birational geometry to prove new lower bounds on the essential dimension of some finite groups.

In this paper, we calculate the Jordan decomposition (or say, the Jordan canonical form) for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix being a Jordan block and the diffusion coefficient matrix…

In this note, we report some recent progress on the Jordan property for (birational) automorphism groups of projective varieties and compact complex varieties.

We introduce the class of modules of constant Jordan type for a finite group scheme $G$ over a field $k$ of characteristic $p > 0$. This class is closed under taking direct sums, tensor products, duals, Heller shifts and direct summands,…