R. Hidalgo

activity

20242026

collaborators

5 papers

math.AG2026

On $p$ -gonal fields of definition

Ruben A. Hidalgo

Let $S$ be a closed Riemann surface of genus $g \geq 2$ and $I ¨ $ be a conformal automorphism of $S$ , of prime order $p$ such that $S / ⟨ I ¨ ⟩$ has genus zero. Let ${\mathb…

math.CV2025

Towards a proof of the Classical Schottky Uniformization Conjecture

RubÃ©n A. Hidalgo

By Koebe's retrosection theorem, every closed Riemann surface of genus $g \geq 2$ is uniformized by a Schottky group. Marden observed that there are Schottky groups that are not cl…

math.AG2025

Generalized superelliptic Riemann surfaces

Ruben A. Hidalgo, SaÃºl Quispe, Tony Shaska

A closed Riemann surface $X$ , of genus $g \geq 2$ , is called a generalized superelliptic curve of level $n \geq 2$ if it admits an order $n$ conformal automorphism $I ¨ $ so…

math.AG2024

Automorphisms of Generalized Fermat manifolds

Ruben A. Hidalgo, Henry F. Hughes, Maximiliano Leyton-Alvarez

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…

math.GT2024

Homology Covers and Automorphisms: Examples

Let $S$ be a Riemann surface with a non-abelian fundamental group and for each integer $k \geq 2$ or $k = \infty$ , let $S_{k}$ be its $k$ -homology cover. The surface $\wi…

On p-gonal fields of definition

Towards a proof of the Classical Schottky Uniformization Conjecture

Generalized superelliptic Riemann surfaces

Automorphisms of Generalized Fermat manifolds

Homology Covers and Automorphisms: Examples

On $p$ -gonal fields of definition