Related papers: On large prime actions on Riemann surfaces

We compute the partition and correlation generating functions for the Heisenberg intertwiner generalized vertex operator algebra on a genus $g$ Riemann surface in the Schottky uniformization. These are expressed in terms of differential…

Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular class of reductive…

We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…

We study surfaces constructed from groups of units in quaternion orders $\Lambda$ over the integers in real quadratic fields k. A short presentation of some general theory of such surfaces is given, in particular, we construct certain…

In previous work, all finite simple groups that act with fixity 4 have been classified. In this article we investigate which ones of these groups act faithfully on a compact Riemann surface of genus at least 2 with fixity four in total and…

We construct polylogarithms on families of pointed Riemann surfaces of any genus which describe monodromies of meromorphic connections with simple poles. Furthermore, we show that the polylogaritms are computable as power series in…

We study a mass formula for Artin--Schreier curves of genus $g$ defined over a finite field $k$ of characteristic $p$. For an odd prime $p$ and for small $g$, we determine the number of $k$-isomorphism classes of Artin-Schreier curves of…

We study the topology of compact manifolds with a Lie group action for which there are only finitely many non-principal orbits, and describe the possible orbit spaces which can occur. If some non-principal orbit is singular, we show that…

The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show that the automorphism group of the fine 1-curve graph is…

We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \PP^1 x \PP^1 we find 17 families which we explicitly describe. We reduce the problem to a…

Let k be an algebraically closed field of characteristic p>0 and C a connected nonsingular projective curve over k with genus g>1. Let (C,G) be a "big action", i.e. a pair (C,G) where G is a p-subgroup of the k-automorphism group of C such…

In [Tohoku Math. J. 62 (2010), 45--53] the second author showed that, except for a few cases, the order $N$ of a cyclic group of self-homeomorphisms of a closed orientable topological surface $S_g$ of genus $g \geq 2$ determines the group…

We study an explicit $(2g-1)$-dimensional family of Jacobian varieties of dimension $\frac{d-1}2(g-1)$, arising from quotient curves of unramified cyclic coverings of prime degree $d$ of hyperelliptic curves of genus $g\ge 2$. By using a…

In this paper the Maxwell field theory is considered on the $Z_n$ symmetric algebraic curves. As a first result, a large family of nondegenerate metrics is derived for general curves. This allows to treat many differential equations arising…

We consider a log-Riemann surface $\mathcal{S}$ with a finite number of ramification points and finitely generated fundamental group. The log-Riemann surface is equipped with a local holomorphic difffeomorphism $\pi : \mathcal{S} \to \C$.…

The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…

The moduli space ${\mathcal{M}}_{g}$, of genus $g\geq2$ closed Riemann surfaces, is a complex orbifold of dimension $3(g-1)$ which carries a natural real structure i.e. it admits an anti-holomorphic involution $\sigma$. The involution…

We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\sigma \geq 2$ is at least quadratic in $\sigma$. We do this through the introduction of a coarse signature space, the space…

We give an algorithm which computes a presentation for a subgroup, denoted $\AM_{g,1,p}$, of the automorphism group of a free group. It is known that $\AM_{g,1,p}$ is isomorphic to the mapping-class group of an orientable genus-$g$ surface…

The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…