Related papers: Quadrangular ${\mathbb Z}_{p}^{l}$-actions on Riem…

Let $\mathrm{Mod}(S_g)$ denote the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. Given a finite subgroup $H$ of $\mathrm{Mod}(S_g)$, let $\mathrm{Fix}(H)$ denote the set of fixed points induced by the action…

We study a class of finite groups $G$ which behave similarly to elementary abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\Aut(G)$.…

In this paper we consider all orientation-preserving $\mathbb{Z}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus $g>0$ for $p$ an odd prime. To do so, we examine particular graphs of groups $(\Gamma($v$),\mathbf{G(v)})$ in…

For $p$ an odd prime number, $q_{0}=p^{t}$, and $q=p^{2t-1}$, let $\mathcal{X}_{\mathcal{G}_{\mathcal{S}}}$ be the nonsingular model of $$ Y^{q}-Y=X^{q_{0}}(X^{q}-X). $$ In the present work, the number of $\mathbb{F}_{q^{n}}$-rational…

In this note we shall determine all actions of groups of prime order p with p > 3 on Gorenstein del Pezzo (singular) surfaces Y of Picard number 1. We show that every order-p element in Aut(Y) (= Aut(Y'), Y' being the minimal resolution of…

Automorphisms of the quantum Schubert cell algebras ${\mathcal U}_q^\pm[w]$ of De Concini, Kac, Procesi and Lusztig and their restrictions to some key invariant subalgebras are studied. We develop some general rigidity results and apply…

We give a detailed description of the algebraic group Aut(g) of automorphisms of a simple finite dimensional Lie superalgebra g over an algebraically closed field k of characteristic 0. We also give a description of the group of…

Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. We give necessary and sufficient conditions on G such that Aut_l(G) = Inn(G).

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…

Let $ G $ be a connected reductive algebraic group over a field $ k $. We study the group of semilinear automorphisms Aut($ G\to $Spec $k$) consisting of algebraic automorphisms of $ G $ over automorphisms of $ k $. We focus on the exact…

The study of algebraic curves $\cX$ with numerous automorphisms in relation to their genus $g(\cX)$ is a well-established area in Algebraic Geometry. In 1995, Irokawa and Sasaki \cite{Sasaki} gave a complete classification of curves over…

An exceptional point in the moduli space of compact Riemann surfaces is a unique surface class whose full automorphism group acts with a triangular signature. A surface admitting a conformal involution with quotient an elliptic curve is…

Let $S$ be a complex smooth projective surface of Kodaira dimension one. We show that the group $\mathrm{Aut}_s(S)$ of symplectic automorphisms acts trivially on the Albanese kernel $\mathrm{CH}_0(S)_\mathrm{alb}$ of the $0$-th Chow group…

A Hurwitz curve is a closed Riemann surface of genus $g \geq 2$ whose group of conformal automorphisms has order $84(g-1)$. In 1895, Wiman proved that for $g=3$ there is, up to isomorphisms, a unique Hurwitz curve; this being Klein's plane…

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…

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…

Let g and p be non-negative integers. Let A(g,p) denote the group consisting of all those automorphisms of the free group on {t_1,...,t_p, x_1,...,x_g, y_1,...y_g} which fix the element t_1t_2...t_p[x_1,y_1]...[x_g,y_g] and permute the set…

We study the {\it arc and curve} complex $AC(S)$ of an oriented connected surface $S$ of finite type with punctures. We show that if the surface is not a sphere with one, two or three punctures nor a torus with one puncture, then the…

Let $X$ be a compact Riemann surface of genus $g\geq 2$, and let $Aut(X)$ be its group of automorphims. We show that the exponent of $Aut(X)$ is bounded by $42(g-1)$. We also determine explicitly the infinitely many values of $g$ for which…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…