Related papers: $(g,k)$-Fermat curves: an embedding of moduli spac…

A non-singular complete irreducible algebraic curve $F_{k,n}$, defined over an algebraically closed field $K$, is called a generalized Fermat curve of type $(k,n)$, where $n, k \geq 2$ are integers and $k$ is relatively prime to the…

A closed Riemann surface $S$ is called a generalized Fermat curve of type $(p,n)$, where $n,p \geq 2$ are integers such that $(p-1)(n-1)>2$, if it admits a group $H \cong {\mathbb Z}_{p}^{n}$ of conformal automorphisms with quotient…

Let ${\cal M}_{g,n}$ and ${\cal H}_{g,n}$, for $2g-2+n>0$, be, respectively, the moduli stack of $n$-pointed, genus $g$ smooth curves and its closed substack consisting of hyperelliptic curves. Their topological fundamental groups can be…

Let $K$ be an algebraically closed field of characteristic $p \geq 0$. A generalized Fermat curve of type $(k,n)$, where $k,n \geq 2$ are integers (for $p \neq 0$ we also assume that $k$ is relatively prime to $p$), is a non-singular…

Let $k,n \geq 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface $S$ that admits a subgroup of conformal automorphisms $H \leq \mbox{Aut}(S)$ isomorphic to $\mathbb{Z}_k^n$, such that the quotient…

A Fuchsian group $\Gamma$ has a modular embedding if its adjoint trace field is a totally real number field and every unbounded Galois conjugate $\Gamma^\sigma$ comes equipped with a holomorphic (or conjugate holomorphic) map ${\phi^\sigma…

If $\Gamma$ is a finitely generated Fuchsian group such that its derived subgroup $\Gamma'$ is co-compact and torsion free, then $S={\mathbb H}^{2}/\Gamma'$ is a closed Riemann surface of genus $g \geq 2$ admitting the abelian group…

Let $d \geq 1$, $k \geq 2$ and $n\geq d+1$ be integers. A $d$-dimensional smooth complex algebraic variety $M$ is called a generalized Fermat variety of type $(d;k,n)$ if there is a Galois holomorphic branched covering $\pi:M \to {\mathbb…

We consider a Fermat curve $F_n:x^n+y^n+z^n=1$ over an algebraically closed field $k$ of characteristic $p\geq0$ and study the action of the automorphism group $G=\left(\mathbb{Z}/n\mathbb{Z}\times\mathbb{Z}/n\mathbb{Z}\right)\rtimes S_3$…

A closed Riemann surface $S$ is called a generalized Fermat curve of type $(p,n)$, where $p,n \geq 2$ are integers, if it admits a group $H \cong {\mathbb Z}_{p}^{n}$ of conformal automorphisms so that $S/H$ is an orbifold of genus zero…

Let $\mathcal{M}_{n,d}$ be the moduli space of semi-stable rank $n$, trace-free Higgs bundles with fixed determinant of degree $d$ on a Riemann surface of genus at least $3$. We determine the following automorphism groups of…

Let $G$ be a connected semisimple group over ${\Bbb Q}$. Given a maximal compact subgroup and a convenient arithmetic subgroup $\Gamma\subset G({\Bbb Q})$, one constructs an arithmetic manifold $S=S(\Gamma)=\Gamma\backslash X$. If $H\subset…

Let $p \geq 3$ be a prime integer and, for $l \geq 1$, let $G \cong {\mathbb Z}_{p}^{l}$ be a group of conformal automorphisms of some closed Riemann surface $S$ of genus $g \geq 2$. By the Riemann-Hurwitz formula, either $p \leq g+1$ or…

A $(\gamma,n)$-gonal pair is a pair $(S,f)$, where $S$ is a closed Riemann surface and $f:S \to R$ is a degree $n$ holomorphic map onto a closed Riemann surface $R$ of genus $\gamma$. If the signature of $(S,f)$ is of hyperbolic type, then…

For any integers $p\geq 2$ and $q\geq 1$, let $\mathbb{H}^{p,q}$ be the pseudo-Riemannian hyperbolic space of signature $(p,q)$. We prove that if $\Gamma$ is the fundamental group of a closed aspherical $p$-manifold, then the set of…

Let $X$ be a compact connected Riemann surface, $D\, \subset\, X$ a reduced effective divisor, $G$ a connected complex reductive affine algebraic group and $H_x\, \subsetneq\, G_x$ a Zariski closed subgroup for every $x\, \in\, D$. A framed…

If $(G,K)$ is a Gelfand pair, with $G$ a Lie group of polynomial growth and $K$ a compact subgroup of $G$, the Gelfand spectrum $\Sigma$ of the bi-$K$-invariant algebra $L^1(K\backslash G/K)$ admits natural embeddings into ${\mathbb R}^n$…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

Let $S_{g,1,p}$ be an orientable surface of genus $g$ with one boundary component and $p$ punctures. Let $\mathcal{M}_{g,1,p}$ be the mapping-class group of $S_{g,1,p}$ relative to the boundary. We construct homomorphisms…

Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…