相关论文: The Cremona group and its subgroups

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.

A random group contains many quasiconvex surface subgroups.

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a…

We classify all finite simple subgroups in the Cremona group of rank 3

Consideration of certain properties of group rings and their ideals search

We give an explicit bound on orders of finite subgroups of Cremona group of rank three over $\mathbb{Q}$.

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 what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.

Various uses of the renormalization group are examined.

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

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

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…

We classify all of the groups with twelve or fewer subgroups. This paper is the proof of the entries in a submission to the Online Encyclopedia of Integer Sequences.

We prove that a finite $3$-group in the Cremona group $\mathrm{Cr}_3(\mathbb{C})$ can be generated by at most $4$ elements. This provides the last missing piece in bounding the ranks of finite $p$-subgroups in the space Cremona group.

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and…

For a group G and positive interger m, Gm denotes the subgroup generated by the elements gm where g runs through G. The subgroups not of the form Gm are called nonpower subgroups. We extend the classification of groups with few nonpower…

In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the real projective plane.

By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…

We study a family of Riemannian problems on the Heisenberg group that tends to the sub-Riemannian problem on this group.