Related papers: 15-nodal quartic surfaces. Part II: The automorphi…
Frucht showed that, for any finite group $G$, there exists a cubic graph such that its automorphism group is isomorphic to $G$. For groups generated by two elements we simplify his construction to a graph with fewer nodes. In the general…
We calculate the automorphism group of certain Enriques surfaces. The Enriques surfaces that we investigate include very general $n$-nodal Enriques surfaces and very general cuspidal Enriques surfaces. We also describe the action of the…
We present some (unfortunately not all) known properties on the Cremona group; when it's possible we mentioned links with the most known group of polynomial automorphisms of the affine plane. The mentioned properties are essentially…
It is well-known that a nonsingular minimal cubic surface is birationally rigid; the group of its birational selfmaps is generated by biregular selfmaps and birational involutions such that all relations between the latter are implied by…
The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…
For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli…
Let Y be a complex Enriques surface whose universal cover X is birational to a general quartic Hessian surface. Using the result on the automorphism group of X due to Dolgachev and Keum, we obtain a finite presentation of the automorphism…
This is a systematic exposition of recent results which completely describe the group of automorphisms and the group of autoequivalences of generic analytic K3 surfaces. These groups, hard to determine in the algebraic case, admit a good…
For a complex surface of general type with a relatively minimal genus 2 fibration, the bounds of the orders of the automorphism group of the fibration, of its abelian subgroups and of its cyclic subgroups are determined as linear functions…
Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of…
It is known that an automorphism group of a K3 surface with Picard number two is either infinite cyclic group or infinite dihedral group if it is infinite. In this paper, we study the generators of an automorphism group. We use the…
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 present the construction of Inoue surfaces of type $S^{(+)}/S^{(-)}$ in terms of data arising from real quadratic number fields. We then describe the automorphism group of such surfaces in terms of this data.
A cyclic $n$-gonal surface is a compact Riemann surface $X$ of genus $g\geq 2$ admitting a cyclic group of conformal automorphisms $C$ of order $n$ such that the quotient space $X/C$ has genus 0. In this paper, we provide an overview of…
The Somos-4 equation defines the sequences with this name. Looking at these sequences with an additional property we get a quartic polynomial in 4 variables. This polynomial defines a rational, projective surface in $\mathbb{RP}^{3}$. Here…
We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
In this paper we study the automorphisms group of some K3 surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study some particlar case of a K3 surface of Picard rank two.
We describe the groups of automorphisms of two generated free braided associative algebras with involutive diagonal braidings over a field of characteristic $\neq 2$. Depending on the form of the diagonal involutive braiding, five different…
We describe all possible arrangements of the ten nodes of a generic real determinantal quartic surface in $\Cp3$ with nonempty spectrahedral region.