Related papers: Genus Zero Actions on Riemann Surfaces

Let X be a finitistic space with non-trivial cohomology groups H^in(X;Z)=Z with generators v_i, where i = 0, 1, 2, 3. We say that X has cohomology type (a, b) if v_1^2 = av_2 and v_1v_2 = bv_3 . In this note, we determine the mod 2…

Any open Riemann surface $R_0$ of finite genus $g$ can be conformally embedded into a closed Riemann surface of the same genus, that is, $R_0$ is realized as a subdomain of a closed Riemann surface of genus $g$. We are concerned with the…

The goal of this paper is to study ergodic and rigidity properties of smooth actions of the discrete Heisenberg group $\H$. We establish the decomposition of the tangent space of any $C^\infty$ compact Riemannian manifold $M$ for Lyapunov…

We classify polar isometric actions on simply connected 3-dimensional Riemannian homogeneous spaces, up to orbit equivalence. In particular, we classify extrinsically homogeneous surfaces in such spaces and study the geometry of the orbit…

We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. Inspired to the recent paper \cite{gb2}, see also \cite{ch} and \cite{pacini}, we study Lagrangian orbits of…

The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the…

Let $X=G/\Gamma$ be the quotient of a semisimple Lie group $G$ by its non-cocompact arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $X$. We give several equivalent algebraic conditions on $H$ for the existence…

Let M be a closed connected oriented manifold admitting a non-zero degree map to a nilmanifold. In the first part of the paper we study effective finite group actions on M. In particular, we prove that Homeo(M) is Jordan, we bound the…

We prove that, given any smooth action of a compact quantum group (in the sense of \cite{rigidity}) on a compact smooth manifold satisfying some more natural conditions, one can get a Riemannian structure on the manifold for which the…

We address the following question: Determine the affine cones over smooth projective varieties which admit an action of a connected algebraic group different from the standard C*-action by scalar matrices and its inverse action. We show in…

In this article, we consider certain irreducible subvarieties of the moduli space of compact Riemann surfaces determined by the specification of actions of finite groups. We address the general problem of determining which among them are…

Given a certain triangulation of a punctured surface with boundary, we construct a new triangulated surface without punctures which covers it. This new surface is naturally equipped with an action of a group of order two, and its quotient…

The odd character variety of a Riemann surface is a moduli space of SO(3) representations of the fundamental group which can be interpreted as the moduli space of stable holomorphic rank 2 bundles of odd degree and fixed determinant. This…

Let $X$ be a smooth manifold belonging to one of these three collections: acyclic manifolds (compact or not, possibly with boundary), compact connected manifolds (possibly with boundary) with nonzero Euler characteristic, integral homology…

An additive action on an algebraic variety is an effective action of the vector group with an open orbit. We describe projective surfaces with du Val singularities that admit an additive action with a finite number of orbits. In particular,…

We study actions of linear algebraic groups on central simple algebras using algebro-geometric techniques. Suppose an algebraic group G acts on a central simple algebra A of degree n. We are interested in questions of the following type:…

Recently there has been renewed interest in the mapping-class group of a compact surface of genus $g \ge 2$ and also in its finite order elements. A finite order element of the mapping-class group will be a conformal automorphisms on some…

Let $\mathcal H_g$ be the moduli space of genus $g$ hyperelliptic curves. In this note, we study the locus $\mathcal L$ in $\mathcal H_g$ of curves admitting a $G$-action of given ramification type $\sigma$ and inclusions between such loci.…

Motivated by the theory of Riemann surfaces and specifically the significance of Weierstrass points, we classify all finite simple groups that have a faithful transitive action with fixity 4, along with details about all possible such…

An effective action is obtained for the $N=1$, $2D-$induced supergravity on a compact super Riemann surface (without boundary) $\hat\Sigma$ of genus $g>1$, as the general solution of the corresponding superconformal Ward identity. This is…