Related papers: Surfaces with given Automorphism Group

We will consider a two dimensional "symmetric" subfamily of the four dimensional family of Fricke cubic surfaces. The main result is that such symmetric cubic surfaces arise as character varieties for the exceptional group of type G_2.…

Let $ 1 \rightarrow N \rightarrow G \rightarrow Q \rightarrow 1$ be an exact sequence of finitely presented groups where Q is infinite and not virtually cyclic, and is the fundamental group of some closed 3-manifold. If G is Kaehler, we…

Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of…

It follows from an observation of A. Coble in 1919 that the automorphism group of an unnodal Enriques surface contains the $2$-congruence subgroup of the Weyl group of the $E_{10}$-lattice. In this article, we determine how much bigger the…

We give several sufficient conditions for a double of a free group along a cyclic subgroup to contain a surface subgroup.

Gordon and Wilton recently proved that the double D of a free group F amalgamated along a cyclic subgroup C of F contains a surface group if a generator w of C satisfies a certain 3-manifold theoretic condition, called virtually…

We prove that the group $\mathrm{SAut}_{\mathrm{k}}(\mathbb{A}^2)$ is simple as an algebraic group of infinite dimension, over any infinite field $\mathrm{k}$, by proving that any closed normal subgroup is either trivial or the whole group.…

Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space $\mathbb R^n$ $(n\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition…

Circulant graphs are a widely studied family of graphs whose members possess varying amounts of symmetry. Although considerable progress has been made in finding the automorphism groups of circulant graphs under certain restrictions, a…

It is known that the automorphism group of any projective K3 surface is finitely generated [24]. In this paper, we consider a certain kind of K3 surfaces with Picard number 3 whose automorphism groups are isomorphic to congruence subgroups…

We prove that the automorphism group of an affine, cubic surface with equation $xyz=g(x,y)$ contains ${\mathbb Z}$ as a finite index subgroup. These equations were first studied by Mordell. v.2: small changes, references updated.

We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group…

Let $$1 \to H \to G \to Q \to 1$$ be an exact sequence where $H= \pi_1(S)$ is the fundamental group of a closed surface $S$ of genus greater than one, $G$ is hyperbolic and $Q$ is finitely generated free. The aim of this paper is to provide…

In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex…

We prove a topological extension of Dirac's theorem suggested by Gowers in 2005: for any connected, closed surface $\mathscr{S}$, we show that any two-dimensional simplicial complex on $n$ vertices in which each pair of vertices belongs to…

Let $S$ be a nonorientable surface of genus $g\ge 5$ with $n\ge 0$ punctures, and $\Mcg(S)$ its mapping class group. We define the complexity of $S$ to be the maximum rank of a free abelian subgroup of $\Mcg(S)$. Suppose that $S_1$ and…

We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a…

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…

In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was…

Let $\AAutH (X)$ be the subgroup of the group $\AutH (X)$ of holomorphic automorphisms of a normal affine algebraic surface $X$ generated by elements of flows associated with complete algebraic vector fields. Our main result is a…