R. A. Hidalgo

activity

20242026

collaborators

10 papers

math.GT2026

Infinite-type Schottky groups and group actions on infinite-type surfaces

Rubén A. Hidalgo

We introduce a certain class of purely loxodromic free Kleinian groups, called infinite-type Schottky groups, which are defined by a suitable collection of simple loops on the Riem…

math.AG2025

$Z_{p}^{m}$ -actions of type $(d; p, n)$

Ruben A. HIdalgo, Maximiliano Leyton-Alvarez

A $Z_{p}^{m}$ -action of type $(d; p, n)$ , where $2 \leq d \leq m \leq n$ are integers, is a pair $(S, N)$ where $S$ is a $d$ -dimensional compact complex manifold, $N \cong {…

math.AG2025

$Z_{k}^{m}$ -actions of signature $(0; k, \dots n + 1, k)$

Rubén A. Hidalgo, Sebastián Reyes-Carocca

An action of a finite group $G$ is a pair $(S, G^)$ , where $S$ is a compact Riemann surface of genus $g ⩾ 2$ and $G^⩽ Aut (S)$ is isomorphic to $G$ .…

math.AG2025

Algebraic models of cyclic $k$ -gonal curves

Ruben A. Hidalgo, Sebastián Reyes-Carocca

In this paper, we describe explicit algebraic equations of tame cyclic $k$ -gonal curves, where $k \geq 2$ is an integer, reflecting the action of the normalizer of a tame cyclic $k…

math.GT2025

Generalized Fermat Riemann surfaces of infinite type

Ruben A. Hidalgo

The Loch Ness monster (LNM) is, up to homeomorphisms, the unique orientable, connected, Hausdorff, second countable surface of infinite genus and with exactly one end. For each int…

math.DS2024

On the FOD/FOM parameter of rational maps

Ruben A. Hidalgo

Let $χ$ be a (right) action of $PSL_{2} (L)$ on the space $L (z)$ of rational maps defined over an algebraically closed field $L$ . If $R \in {\mat…

math.GT2024

The structure of MDC-Schottky extension groups

Rubén A. Hidalgo

Let $M^{0}$ be a complete hyperbolic $3$ -manifold whose conformal boundary is a closed Riemann surface $S$ of genus $g \geq 2$ . If $M = M^{0} \cup S$ , then let $Aut (S; M)$ be th…

math.CV2024

A simple remark on holomorphic maps on Torelli space of marked spheres

Ruben A. Hidalgo

The configuration space of $k \geq 3$ ordered points in the Riemann sphere $C$ is the Torelli space $U_{0, k}$ ; a complex manifold of dimension $k - 3$ . I…

math.AG2024

Uniqueness of Generalized Fermat Groups in positive characteristic

Rubén A. Hidalgo, Henry F. Hughes, Maximiliano Leyton-Álvarez

Let $X \subset P_{K}^{m}$ be a smooth irreducible projective algebraic variety of dimension $d$ , defined over an algebraically closed field $K$ of characteristic $p > 0$ . We…

math.AG2024

Computing the Field of moduli of some non-hyperelliptic pseudo-real curves

Ruben A. Hidalgo

The explicit computation of the field of moduli of a closed Riemann surface is, in general, a difficult task. In this paper, for each even integer $k \geq 2$ , we consider a suitabl…

Infinite-type Schottky groups and group actions on infinite-type surfaces

Zpm​-actions of type (d;p,n)

Zkm​-actions of signature (0;k,…n+1,k)

Algebraic models of cyclic k-gonal curves

Generalized Fermat Riemann surfaces of infinite type

On the FOD/FOM parameter of rational maps

The structure of MDC-Schottky extension groups

A simple remark on holomorphic maps on Torelli space of marked spheres

Uniqueness of Generalized Fermat Groups in positive characteristic

Computing the Field of moduli of some non-hyperelliptic pseudo-real curves

$Z_{p}^{m}$ -actions of type $(d; p, n)$

$Z_{k}^{m}$ -actions of signature $(0; k, \dots n + 1, k)$

Algebraic models of cyclic $k$ -gonal curves