Related papers: Automorphism groups of pseudoreal Riemann surfaces

We compute the automorphism groups of the Dolbeault, de Rham and Betti moduli spaces for the multiplicative group ${\mathbb C}^*$ associated to a compact connected Riemann surface.

We show that every irreducible, simply connected curve on a toric affine surface X over the field of complex numbers is an orbit closure of a multiplicative group action on X. It follows that up to the action of the automorphism group…

Let $S$ be a hyperbolic oriented Riemann surface of finite type. The main purpose of this paper is to show that non-trivial geometric intersection between closed curves on $S$ is detected by some symplectic submodules they naturally…

Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to…

For a real semisimple Lie algebra, we consider its automorphism group quotient by its identity component. This is known as the outer automorphism group. In this article, we compute the outer automorphism groups of all real semisimple Lie…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

In this paper, we prove that the group $\mathrm{Aut}_\mathbb{Q}(X)$ of numerically trivial automorphisms are uniformly bounded for smooth projective threefolds $X$ of general type which either satisfy $q(X)\geq 3$ or have a Gorenstein…

The concept of an adapted homology basis for a prime order conformal automorphism of a compact Riemann surface extends to arbitrary finite groups of conformal automorphisms. Here we compute some examples of adapted homology bases for some…

In this article we consider Riemann surfaces and abelian varieties endowed with a group of automorphisms isomorphic to a generalized quaternion group. We provide isogeny decompositions of each abelian variety with this action, compute…

In this paper, we prove that each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface. We deduce, from this result, that the group of…

In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem…

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…

Let $S$ be a smooth minimal complex surface of general type with $p_g=0$ and $K^2=7$. We prove that any involution on $S$ is in the center of the automorphism group of $S$. As an application, we show that the automorphism group of an Inoue…

We prove that the outer automorphism group of a one-ended hyperbolic group is virtually a hierarchically hyperbolic group (HHG), under mild orientability conditions on the associated JSJ decomposition. This is done by proving that a…

Given integers $d\ge 3$ and $N\ge 3$. Let $G$ be a finite abelian group acting faithfully and linearly on a smooth hypersurface of degree $d$ in the complex projective space $\mathbb{P}^{N-1}$. Suppose $G\subset PGL(N, \mathbb{C})$ can be…

An automorphism of a group G is called an IA-automorphism if it induces the identity automorphism on the abelianized group G/G'. Let IA(G) denote the group of all IA-automorphisms of G. We classify all finitely generated nilpotent groups G…

Let ${\cal M}_{g,[n]}$, for $2g-2+n>0$, be the D-M moduli stack of smooth curves of genus $g$ labeled by $n$ unordered distinct points. The main result of the paper is that a finite, connected \'etale cover ${\cal M}^\l$ of ${\cal…

For a finite alphabet $\mathcal{A}$ and shift $X\subseteq\mathcal{A}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group ${\rm Aut}(X)$. For such systems, we…

We give a condition on the defining graph of a right-angled Artin group which implies its automorphism group is virtually indicable, that is, it has a finite-index subgroup that admits a homomorphism onto $\Z$. We use this as part of a…

Belolipetsky and Jones classified those compact Riemann surfaces of genus $g$ admitting a large group of automorphisms of order $\lambda (g-1)$, for each $\lambda >6,$ under the assumption that $g-1$ is a prime number. In this article we…