Sebastián Reyes‐Carocca

activity

20122026

most citedOn the one-dimensional family of Riemann surfaces of genus

q

with

4 q

automorphisms

15 citations · 122 across the 31 of their papers we have counts for

collaborators

34 papers

math.AG2026

A classification of triangular Riemann surfaces with $2 p^{2}$ automorphisms

Sebastián Reyes-Carocca, Yazmin Rivera Nene

In this article we provide a classification and description of compact Riemann surfaces admitting a triangular action of a group of order $2 p^{2},$ where $p$ is an odd prime number.…

math.CO2025

On orientably-regular maps of Euler characteristic $- 2 p^{2}$

Tomás Foncea E., Sebastián Reyes-Carocca

In this article, we study orientably-regular maps of Euler characteristic $- 2 p^{2}$ and classify those that admit a group of orientation-preserving automorphisms of order $10 p^{2}$ , wh…

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.AG2025

A generalisation of the pencil of Kuribayashi-Komiya quartics

Valentina Moreno Vega, Sebastián Reyes-Carocca

The pencil of Kuribayashi-Komiya quartics $$ x^4 + y^4 + z^4 + t(x^2y^2 + x^2z^2 + y^2z^2)=0 \, \mbox{ where } t \in \bar{\mathbb{C}} $$is a complex one-dimensional family of Riema…

math.AG2025

The locus of Riemann surfaces of genus $2 (p - 1)$ with $4 p$ automorphisms

Angel Carocca, Sebastián Reyes-Carocca

Let $p ⩾ 5$ be a prime number. In this article we provide a complete and explicit description of the locus formed by the compact Riemann surfaces of genus $2 (p - 1)$ that are…

math.AG2024

On Dihedral Group Actions on Riemann Surfaces

Pablo Alvarado-Seguel, Sebastián Reyes-Carocca

This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence…

math.AG2024

On the Jacobian variety of the Accola-Maclachlan curve of genus four

Robert Auffarth, Sebastián Reyes-Carocca, Anita M. Rojas

In this short note, we study the Jacobian variety of the Accola-Maclachlan curve of genus four and obtain explicitly its Poincaré isogeny decomposition. More precisely, we show tha…

math.AG2023

Classifying compact Riemann surfaces by number of symmetries

Sebastián Reyes-Carocca, Pietro Speziali

In this article we consider compact Riemann surfaces that are uniquely determined by the property of possessing a group of automorphisms of a prescribed order, strengthening unique…

math.AG2023★ 1 cited

On non-normal subvarieties of the moduli space of Riemann surfaces

Rubén A. Hidalgo, Jennifer Paulhus, Sebastián Reyes-Carocca +1

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 addres…

math.AG2022★ 1 cited

Infinitely many Riemann surfaces with transitive action on Weierstrass points

Sebastián Reyes-Carocca, Pietro Speziali

In this short note, we prove the existence of infinitely many pairwise non-isomorphic non-hyperelliptic Riemann surfaces with automorphism group acting transitively on the Weierstr…

math.AG2021

Abelian varieties and Riemann surfaces with generalized quaternion group action

Angel Carocca, Sebastián Reyes-Carocca, Rubí E. Rodríguez

In this article we consider Riemann surfaces and abelian varieties endowed with a group of automorphisms isomorphic to a generalized quaternion group. We provide isogeny decomposit…

math.AG2020

A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication

Sebastián Reyes-Carocca

Let $m ⩾ 6$ be an even integer. In this short note we prove that the Jacobian variety of a quasiplatonic Riemann surface with associated group of automorphisms isomorphic t…

math.AG2020★ 1 cited

On large prime actions on Riemann surfaces

Sebastián Reyes-Carocca, Anita M. Rojas

In this article we study compact Riemann surfaces of genus $g$ with an automorphism of prime order $g + 1.$ The main result provides a classification of such surfaces. In addition, w…

math.AG2020

A family of $(p, n)$ -gonal Riemann surfaces with several $(p, n)$ -gonal groups

Sebastián Reyes-Carocca

Let $p ⩾ 3$ be a prime number and let $n ⩾ 0$ be an integer such that $p - 1$ divides $n .$ In this short note we construct a family of $(p, n)$ -gonal Riemann surfaces…

math.AG2020★ 3 cited

On $pq$ -fold regular covers of the projective line

Sebastián Reyes-Carocca

Let $p$ and $q$ be odd prime numbers. In this paper we study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provid…

math.AG2020★ 9 cited

On families of Riemann surfaces with automorphisms

Milagros Izquierdo, Sebastián Reyes-Carocca, Anita M. Rojas

In this article we determine the maximal possible order of the automorphism group of the form $a g + b$ , where $a$ and $b$ are integers, of a complex three and four-dimensional fami…

math.AG2020

Nilpotent groups of automorphisms of families of Riemann surfaces

Sebastián Reyes-Carocca

In this article we extend results of Zomorrodian to determine upper bounds for the order of a nilpotent group of automorphisms of a complex $d$ -dimensional family of compact Rieman…

math.AG2020

Groups of automorphisms of Riemann surfaces and maps of genus $p + 1$ where $p$ is prime

Milagros Izquierdo, Gareth A. Jones, Sebastián Reyes-Carocca

We classify compact Riemann surfaces of genus $g$ , where $g - 1$ is a prime $p$ , which have a group of automorphisms of order $ρ (g - 1)$ for some integer $ρ \geq 1$ , and determine isogen…

math.AG2020

Complex surfaces with mutually non-biholomorphic universal covers

Gabino González-Diez, Sebastián Reyes-Carocca

It is known that the universal cover of compact Riemann surface is either the projective line, the complex plane or the unit disk. In this article we construct a very explicit fami…

math.AG2019

Riemann surfaces of genus $1 + q^{2}$ with $3 q^{2}$ automorphisms

Angel Carocca, Sebastián Reyes-Carocca

In this article we classify compact Riemann surfaces of genus $1 + q^{2}$ with a group of automorphisms of order $3 q^{2},$ where $q$ is a prime number. We also study decompositions of th…

math.AG2018★ 9 cited

On Riemann surfaces of genus $g$ with $4 g - 4$ automorphisms

Sebastián Reyes-Carocca

In this article we study compact Riemann surfaces with a non-large group of automorphisms of maximal order; namely, compact Riemann surfaces of genus $g$ with a group of automorphi…

math.AG2018★ 13 cited

A note on large automorphism groups of compact Riemann surfaces

Milagros Izquierdo, Sebastián Reyes-Carocca

Belolipetsky and Jones classified those compact Riemann surfaces of genus $g$ admitting a large group of automorphisms of order $λ (g - 1)$ , for each $λ > 6,$ under the assumption that…

math.AG2018★ 15 cited

On the one-dimensional family of Riemann surfaces of genus $q$ with $4 q$ automorphisms

Sebastián Reyes-Carocca

Bujalance, Costa and Izquierdo have recently proved that all those Riemann surfaces of genus $g \geq 2$ different from $3, 6, 12, 15$ and 30, with exactly $4 g$ automorphisms form an…

A classification of triangular Riemann surfaces with 2p2 automorphisms

On orientably-regular maps of Euler characteristic −2p2

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

Algebraic models of cyclic k-gonal curves

A generalisation of the pencil of Kuribayashi-Komiya quartics

The locus of Riemann surfaces of genus 2(p−1) with 4p automorphisms

On Dihedral Group Actions on Riemann Surfaces

On the Jacobian variety of the Accola-Maclachlan curve of genus four

Classifying compact Riemann surfaces by number of symmetries

On non-normal subvarieties of the moduli space of Riemann surfaces

Infinitely many Riemann surfaces with transitive action on Weierstrass points

Abelian varieties and Riemann surfaces with generalized quaternion group action

A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication

On large prime actions on Riemann surfaces

A family of (p,n)-gonal Riemann surfaces with several (p,n)-gonal groups

On pq-fold regular covers of the projective line

On families of Riemann surfaces with automorphisms

Nilpotent groups of automorphisms of families of Riemann surfaces

Groups of automorphisms of Riemann surfaces and maps of genus p+1 where p is prime

Complex surfaces with mutually non-biholomorphic universal covers

Riemann surfaces of genus 1+q2 with 3q2 automorphisms

On Riemann surfaces of genus g with 4g−4 automorphisms

A note on large automorphism groups of compact Riemann surfaces

On the one-dimensional family of Riemann surfaces of genus q with 4q automorphisms

A classification of triangular Riemann surfaces with $2 p^{2}$ automorphisms

On orientably-regular maps of Euler characteristic $- 2 p^{2}$

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

Algebraic models of cyclic $k$ -gonal curves

The locus of Riemann surfaces of genus $2 (p - 1)$ with $4 p$ automorphisms

A family of $(p, n)$ -gonal Riemann surfaces with several $(p, n)$ -gonal groups

On $pq$ -fold regular covers of the projective line

Groups of automorphisms of Riemann surfaces and maps of genus $p + 1$ where $p$ is prime

Riemann surfaces of genus $1 + q^{2}$ with $3 q^{2}$ automorphisms

On Riemann surfaces of genus $g$ with $4 g - 4$ automorphisms

On the one-dimensional family of Riemann surfaces of genus $q$ with $4 q$ automorphisms