相关论文: The Jordan property of Cremona groups and essentia…

We prove that the group of birational automorphisms of a geometrically irreducible algebraic surface over a finite field is Jordan. We show that the analogous statement fails in higher dimensions. Finally, we prove that groups of birational…

The Cremona dimension of a group $G$ is the minimal $n$ such that $G$ is isomorphic to a subgroup of the Cremona group of birational transformations of an $n$-dimensional rational variety. In this survey article, we give many examples that…

We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…

Assuming a particular case of Borisov--Alexeev--Borisov conjecture, we prove that finite subgroups of the automorphism group of a finitely generated field over Q have bounded orders. Further, we investigate which algebraic varieties have…

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.

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 $8$.

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

We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index one covers for $n$-dimensional klt singularities. We give an…

The notion of a topological Jordan decomposition of a compact element of a reductive p-adic group has proven useful in many contexts. In this paper, we generalise it to groups defined over fairly general discretely-valued fields and prove…

We determine three-dimensional algebraic varieties whose groups of birational selfmaps do not satisfy the Jordan property.

We prove that the image of the pluricanonical representation of a group of bimeromorphic automorphisms of a complex manifold has bounded finite subgroups. As a consequence, we show that the group of bimeromorphic automorphisms of an…

In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…

We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of algebraic surfaces. This gives a positive answer to a question of Vladimir L. Popov.

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

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…

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

The Cremona group of rank n over a field k is the group of birational automorphisms of the n-dimensional projective space over the field k. We study the minimal dimension such that all finite subgroups of the Cremona group have a faithful…

We compute the Jordan constant for the group of birational automorphisms of a projective plane $\mathbb{P}^2_{\mathbb k}$, where ${\mathbb k}$ is either an algebraically closed field of characteristic 0, or the field of real numbers, or the…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.