Related papers: Automorphisms of parabolic Inoue surfaces

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

We construct first examples of discrete geometrically finite subgroups of PU(2,1) which contain parabolic elements, and are isomorphic to surface groups.

We investigate the action of the automorphism group of a closed Riemann surface on its set of theta characteristics (or spin structures). We give criteria for when an automorphism fixes all spin structures, or when it fixes just one. The…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

We classify real two-dimensional orbits of conformal subgroups such that the orbits contain two circular arcs through a point. Such surfaces must be toric and admit a M\"obius automorphism group of dimension at least two. Our theorem…

This paper shows that the automorphism group of a Beauville surface is a finite solvable group, and describes its possible structure. It relies on results of Singerman on triangle group inclusions, and of Lucchini on generators for special…

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…

The structure of the automorphism group of the sandwich semigroup IS_n is described in terms of standard group constructions.

We determine the detailed structure of parabolic subgroups of orthogonal groups over $\mathbb{Z}$, and deduce the precise form of canonical boundary components in toroidal compactifications of orthogonal Shimura varieties.

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of…

Building on work of Farb and the second author, we prove that the group of automorphisms of the fine curve graph for a surface is isomorphic to the group of homeomorphisms of the surface. This theorem is analogous to the seminal result of…

In this paper, we briefly review some of the known results concerning the cohomological structures of the mapping class group of surfaces, the outer automorphism group of free groups, the diffeomorphism group of surfaces as well as various…

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…

In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.

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…

In previous work we determined automorphism groups of cyclic algebraic curves defined over fields of any odd characteristic. In this paper we determine parametric equations of families of curves for each automorphism group for such curves.

We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class group of that surface.

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

We present a description for the automorphism groups of Du Val del Pezzo surfaces whose automorphism groups are infinite.