Related papers: Automorphism groups of cubic fivefolds and fourfol…

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…

Let $F(x, y)$ be a binary form of degree at least three and non-zero discriminant. In this article we compute the automorphism group $\operatorname{Aut} F$ for four families of binary forms. The first two families that we are interested in…

We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of…

The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between…

Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.

In this paper, we investigate some characteristic features of holomorphic semigroups. In particular, we investigate nice examples of holomorphic semigroups whose every left or right ideal includes minimal ideal. These examples are compact…

We give a sharp bound on the number of automorphisms of a stable curve of a given genus and describe all curves attaining this bound.

A monomial algebra B is defined as a quotient of a polynomial ring by a monomial ideal, which is an ideal generated by a finite set of monomials. In this paper, we determine the automorphism group of a monomial algebra B, under the…

Quadratic automorphisms of $\mathbb C^3$ are classified up to affine conjugacy into seven classes by Forn$\ae$ss and Wu. Five of them contain irregular maps with interesting dynamics. In this paper, we focus on the maps in the fifth class…

Let $X$ be a compact Riemann surface of genus $g\geq 2$. Let $Aut(X)$ be its group of automorphisms and $G\subseteq Aut(X)$ a subgroup. Sharp upper bounds for $|G|$ in terms of $g$ are known if $G$ belongs to certain classes of groups, e.g.…

Let F be a local field of positive characteristic, and let G be either a Heisenberg group over F, or a certain (nonabelian) two-dimensional unipotent group over F. If H is an arithmetic subgroup of G, we provide an explicit description of…

In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for…

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving…

We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with…

It is clear that the full automorphism group of the $(15,8,4)$-design of points and hyperplane complements of ${\rm PG}(3,2)$ is ${\rm GL}(4,2)$. Using methods of point-line geometries, we determine the full automorphism groups of the…

In this article we determine the maximal possible order of the automorphism group of the form $ag + b$, where $a$ and $b$ are integers, of a complex three and four-dimensional family of compact Riemann surfaces of genus $g$, appearing for…

We determine all holomorphically separable complex manifolds of dimension $p+q$ which admits a smooth envelope of holomorphy such that the general indefinite unitary group of size $p+q$ acts effectively by holomorphic transformations. Also…

We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…

We compute the automorphisms groups of all numerical Godeaux surfaces, i.e. minimal smooth surfaces of general type with K^2 = 1 and p_g = 0, with torsion of the Picard group of order \nu equals 3, 4, or 5. We present explicit…