Sebastián Reyes Carocca
Departamento de Matemáticas
Facultad de Ciencias
Universidad de Chile
Santiago, Chile
E-mail address:
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Publicaciones/Publications
Publicaciones/Publications
On dihedral group actions on Riemann surfaces
(joint work with Pablo Alvarado-Seguel)
To appear in Moscow Math. J.
Link
A generalisation of the pencil of Kuribayashi-Komiya quartics
(joint work with Valentina Moreno Vega)
J. of Algebra 694 (2026), 359-380.
doi: 10.1016/j.jalgebra.2026.01.033
Classifying compact Riemann surfaces by number of symmetries
(joint work with P. Speziali)
Manuscripta Math. 176 (2025), no. 2, Paper No. 18.
doi: 10.1007/s00229-025-01618-x
On non-normal subvarieties of the moduli space of Riemann surfaces
(joint work with R. A. Hidalgo, J. Paulhus and A. M. Rojas)
To appear in Transf. Groups (2024)
doi: 10.1007/s00031-024-09870-3
Infinitely many Riemann surfaces with transitive action on Weierstrass points
(joint work with P. Speziali)
Bull. London Math. Soc. 56, no.8, 2625-2633 (2024)
doi: 10.1112/blms.13088
Abelian varieties and Riemann surfaces with generalized quaternion group action
(joint work with A. Carocca and R. E. Rodríguez)
J. Pure Applied Algebra 227, 11, (2023) 107398.
doi: 10.1016/j.jpaa.2023.107398
On large prime actions on Riemann surfaces
J. Group Theory 25 (5), 887-940 (2022)
doi: 10.1515/jgth-2020-0140
(joint work with A. M. Rojas)
Nilpotent groups of automorphisms of families of Riemann surfaces
Ann. Mat. Pura Appl. 201, 359–377 (2022)
doi: 10.1007/s10231-021-01119-0
Riemann surfaces of genus 1+q^2 with 3q^2 automorphisms
J. Algebra 588, 440-470 (2021)
doi: 10.1016/j.jalgebra.2021.09.001
(joint work with A. Carocca)
Groups of automorphisms of Riemann surfaces and maps of genus p+1 where p is prime
Ann. Fenn. Math. 46 (2), 839–867 (2021).
doi: 10.5186/aasfm.2021.4649
(joint work with M. Izquierdo and G. A. Jones).
A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication
Geom. Dedicata 213, 245–249 (2021)
doi: 10.1007/s10711-020-00577-9
On families of Riemann surfaces with automorphisms
J. Pure Applied Algebra 224 no. 10, 106704 (2021)
doi: 10.1016/j.jpaa.2021.106704
(joint work with M. Izquierdo and A. M. Rojas)
On pq-fold regular covers of the projective line
Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115, 23 (2021)
doi: 10.1007/s13398-020-00965-6
A family of (p,n)-gonal Riemann surfaces with several (p,n)-gonal groups
Arch. Math. (Basel) 116 (2021), no. 3, 302-305.
doi: 10.1007/s00013-020-01548-y
On Riemann surfaces of genus g with 4g-4 automorphisms
Israel J. Math. 237, 415–436 (2020)
doi: 10.1007/s11856-020-2010-3
A note on large automorphism groups of compact Riemann surfaces
J. Algebra 547 (2020), 1-21.
(joint work with M. Izquierdo)
doi: 10.1016/j.jalgebra.2019.11.012
On Jacobians with group actions and coverings
Math. Z. 294 (2020) 209-227
doi: 10.1007/s00209-019-02263-3
(joint work with R. E. Rodríguez)
A generalisation of Kani-Rosen decomposition theorem for Jacobian varieties
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), no. 2, 705–722.
doi: 10.2422/2036-2145.201706_003
(joint work with R. E. Rodríguez)
On the one-dimensional family of Riemann surfaces of genus q with 4q automorphisms
J. of Pure and Appl. Algebra 223, no. 5 (2019), 2123-2144.
doi: 10.1016/j.jpaa.2018.07.011
On the connectednes of the moduli space of principally polarized abelian varieties
Moscow Math. J. 18 (2018) , no. 3, 473-489.
doi: 10.17323/1609-4514-2018-18-3-473-489
(joint work with R. E. Rodríguez)
Families of Riemann surfaces, uniformization and arithmeticity
Trans. Amer. Math. Soc. 370 (2018), no. 3, 1529–1549.
doi: 10.1090/tran/6988
(joint work with G. González-Diez)
Quasiplatonic curves with symmetry group Z_2^2 \rtimes Z_m are definable over Q
Bull. London Math. Soc. 49 (2017) 165–183
doi: 10.1112/blms.12014
(joint work with R. A. Hidalgo, L. Jiménez and S. Quispe)
The arithmeticity of a Kodaira fibration is determined by its universal cover
Comment. Math. Helv. 90 (2015), no. 2, 429-434
doi: 10.4171/CMH/359
(joint work with G. González-Diez)
Field of moduli and generalized Fermat curves
Rev. Colombiana Mat. 47 (2013), no. 2, 205-221
(joint work with R. A. Hidalgo and M. E. Valdés).
Fields of moduli of classical Humbert curves
Q. J. Math. 63 (2012), no. 4, 919-930
doi: 10.1093/qmath/har017
(joint work with R. A. Hidalgo)
Field of moduli of generalized Fermat curves
Q. J. Math. (2012), no. 2, 467-475.
doi: 10.1093/qmath/haq049
Publications in conference proceedings
On the Jacobian variety of the Accola-Maclachlan curve of genus four
(joint work with R. Auffarth and A. M. Rojas)
New tools in mathematical analysis and applications, 3–15, Trends Math., Trends Math. Res. Perspect., Birkhäuser/Springer
https://doi.org/10.1007/978-3-031-77050-0_1
Complex surfaces with mutually non-biholomorphic universal covers
Contemp. Math. 766, 153-162 (2021)
doi: 10.1090/conm/766/15380
(joint work with G. González-Diez)
Weil's Galois descent theorem; a computational point of view
Contemp. Math. 766, 217-228 (2021)
doi: 10.1090/conm/766/15383
(joint work with R. A. Hidalgo).
Fiber products of Riemann surfaces
Contemp. Math. 776, 161-175 (2022)
doi: 10.1090/conm/776/15611
(joint work with R. A. Hidalgo and A. Vega)
Proyectos/Projects
Proyectos/Projects
Ongoing
2026 - 2030, FONDECYT Regular Grant 1260144, Automorphisms of Riemann surfaces, Klein surfaces and Jacobian varieties, Principal Researcher
2023 - 2027, FONDECYT Regular Grant 1230708, The geometry of the moduli space of abelian varieties, Co-researcher.
Finished
2022 - 2026, FONDECYT Regular Grant 1220099, Group actions on Riemann surfaces and abelian varieties. Principal Researcher
2023-2024, MATH-AMSUD The geometry of varieties: Group actions, symmetries, moduli and beyond, France, Brazil, Ecuador & Chile.
2019 - 2023, FONDECYT Regular Grant 1190991, The geometry of abelian varieties with group action, Co-researcher.
2021 - 2023, MATH-AMSUD, MATH2020014, 21-MATH-02, Algebraic and geometric aspects of varieties and manifolds, Argentina, Brazil, Chile & France, Researcher.
2020 - 2022, ANID-PCI 190140 Redes Internacionales, South-North Latin American network through Geometry, Universidad de La Frontera & CIMAT, Researcher.
2020 - 2022, ANID-PCI 190145 Redes Internacionales, Joint USA-CHILE Geometry at the Frontier, Universidad de La Frontera & Stony Brook University, Researcher.
2018 - 2021, FONDECYT Iniciación Grant 11180024, The geometry of Riemann surfaces and abelian varieties, Principal Researcher
2018 - 2020, CONICYT-PCI Redes Grant for International Networks 170071, Superficies de Riemann y variedades abelianas con automorfismos, Principal Researcher.
2015 - 2018, FONDECYT Postdoctoral Grant 3160002, Algebraic varieties and their field of definition, Principal Researcher.
2015 - 2018, CONICYT-PIA ANILLO ACT1415, Geometría en la Frontera, Researcher.
Charlas/Talks
Charlas/Talks
International conferences and workshops
Field of moduli of Beauville surfaces
Workshop on low dimensional conformal structures and their groups, University of Gdánsk, Gdánsk, Poland, 2012.
Arithmetic Kodaira Fibrations
Celebration of the Chilean Complex Geometry Group, Universidad de la Frontera, Temuco, Chile, 2014.
On the Arithmeticity of Kodaira Fibrations
Congreso de la Real Sociedad Española de Matemática, Universidad de Granada, Granada, España, 2015.
Movimientos holomorfos y uniformización de familias de superficies de Riemann
Perspectives in Geometry 2, Universidad de La Frontera, Temuco, Chile, 2015.
On quasiplatonic Riemann surfaces with Z_2^2 \rtimes Z_m symmetry
Joint Meeting UAM-UFRO: Superficies de Riemann de tipo finito, Universidad Autónoma de Madrid, Madrid, España, 2016.
A generalisation of Kani-Rosen decomposition theorem for Jacobian varieties
Primer Encuentro SOMACHI-UMA, Valparaíso, Chile, 2016.
Jacobian varieties with group action: a generalisation of Kani-Rosen decomposition theorem
Joint Meeting of the Catalan, Spanish and Swedish Math Societies, Umea, Sweden, 2017.
On the singular sublocus of the moduli space of principally polarized abelian varieties admitting an involution
Coloquio Latinoamericano de Algebra, Quito, Ecuador, 2017.
On the connectedness of the singular locus of the moduli space of principally polarized abelian varieties
Seventh Iberoamerican Congress on Geometry, Universidad de Valladolid, Valladolid, España, 2018.
On the one-dimensional family of Riemann surfaces of genus q with 4q automorphisms
AMS Sectional Meeting, Special Session Automorphisms of Riemann Surfaces and Related Topics, Portland, United States, 2018.
On large automorphism groups of compact Riemann surfaces
Congreso Bienal de la Real Sociedad de Matemática Española, Santander, España, 2019.
Riemann surfaces and abelian varieties with group action
Segundo Encuentro SUMA, Mendoza, Argentina, 2019.
On large prime actions on Riemann surfaces
ECOS-ANID workshop in Algebraic Geometry, Universidad de Poitiers - Universidad de La Frontera, 2020 (online).
pq-fold regular covers of the projective line
South-North Latin American Workshop on Geometry I, UFRO-CIMAT meeting, 2021 (online)
On compact Riemann surfaces and hypermaps of genus p + 1 where p is prime
8th European Congress of Mathematics, Portoroz, Slovenia, 2021 (online).
Abelian varieties and Riemann surfaces with generalized quaternion group action
MathAmSud Workhop "Algebraic and geometric aspects of varieties and manifolds" (online)
Nilpotent groups of automorphisms of Riemann surfaces
AMS Sectional Meeting, Special Session Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics, Tufts, United States, 2022.
A decomposition of Jacobian varieties of certain q^2-gonal Riemann surfaces
Conformal Geometry and Low Dimensional Manifolds: a hybrid Conference in Honour of Antonio F. Costa, Avila, Spain, 2022.
On transitive group actions on Weierstrass points of Riemann surfaces
Workshop Geometry 3 1/2, Universidad de La Frontera, Pucón, Chile, 2022
On non-normal subvarieties of the moduli space of Riemann surfaces
Workshop: Geometry of Riemann Surfaces, Universidad autónoma de Madrid, Spain, 2023
On group action on Riemann surfaces and Weierstrass points
14th ISAAC Congress 2023, Ribeirao Preto, Brasil, 2023.
On non-normal subvarieties of the moduli space of Riemann surfaces
MathAmSud Workshop on Algebraic Geometry, Université Côte d'Azur, Nice, France, 2024
Una introducción a las superficies de Riemann con automorfismos
Escuela "Geometría desde la Mitad del Mundo”, Universidad Central del Ecuador, 2024
On subvarieties of the moduli space of Riemann surfaces determined by group actions
Campinas, 2024
Z_k^m-actions of signature (0; k, ..., k)
Congreso Bienal de la Real Sociedad Matemática Española, Alicante, 2026.
Local conferences and workshops
Superficies de Riemann y cuerpos de definición
VII Encuentro de Geometría Compleja y Sistemas Dinámicos, Universidad Técnica Federico Santa María, Valparaíso, Chile, 2009.
Sobre el cuerpo de módulos y de definición para ciertas curvas de Fermat generalizadas
LXXIX Encuentro Anual de la Sociedad de Matemática de Chile, Olmué, Chile, 2009.
Cuerpos de módulos para curvas de Fermat generalizadas
XX Congreso de Matemática Capricornio, Universidad de Tarapacá, Arica, Chile, 2010.
Beauville surfaces and their fields of moduli
X Encuentro de Geometría Compleja y Sistemas Dinámicos, Universidad Técnica Federico Santa María, Valparaíso, Chile, 2012.
Superficies algebraicas; uniformización y aritmeticidad
LXXXIV Encuentro Anual de la Sociedad de Matemática de Chile, Pucón, Chile, 2015.
Quasiplatonic curves with symmetry Z_2^2 \rtimes Z_m are definable over Q
Jornadas de Matemática de la Zona Sur 2016, Universidad de Talca, Santa Cruz, Chile, 2016.
Jacobians with group action and coverings
Jornadas de Matemática de la Zona Sur 2017, Universidad Católica de la Santísima Concepción, Concepción, Chile, 2017.
On the one-dimensional family of Riemann surfaces of genus q with 4q automorphisms
Encuentro Anual SOMACHI 2017, Universidad de Talca, Chile.
Variedades abelianas con acción de grupo
Encuentro de Sistemas Dinámicos, Geometría Compleja y Geometría Aritmética, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile, 2017.
On quasiplatonic Riemann surfaces with complex multiplication
Jornadas de Matemática de la Zona Sur 2018, Universidad Austral de Chile, Valdivia, Chile.
Superficies de Riemann y variedades abelianas con automorfismos
Encuentro Anual SOMACHI 2018, Universidad de O'Higgins, Rancagua, Chile, 2018.
Superficies de Riemann de género g con λ(g − 1) automorfismos
Jornadas de Matemática de la Zona Sur 2019, Universidad de Magallanes, Punta Arenas, Chile.
A family of (p,n)-gonal Riemann surfaces with several (p,n)-gonal groups
Jornadas de Matemática de la Zona Sur, Universidad de Los Lagos (online), 2022.
Acciones de grupos en superficies de Riemann
Workshop Geometría Compleja y Aplicaciones, UTFSM, Valparaíso, 2022
Sobre ciertas subvariedades del espacio de módulos de superficies de Riemann
Jornadas de Matemática de la Zona Sur, Universidad de Concepción, 2023
Clasificando superficies de Riemann compactas por su número de simetrías.
Encuentro Anual SOMACHI 2023, Universidad de Chile, Santiago de Chile, Chile, 2023.
Seminars
Arithmetic Kodaira Fibrations
Seminar of the Department of Mathematics, University of Linköping, Linköping, Sweden, 2014.
Families of Riemann surfaces, uniformization and arithmeticity
Seminario Cruz del Sur, Universidad de La Frontera, Temuco, Chile, 2015.
Un pincel de curvas con acción de DpxDp
Tercera sesión de trabajo, Proyecto Anillo ACT1415, PIA-CONACYT, 2016.
Sobre ciertas superficies de Riemann definidas sobre Q
Seminario Cruz del Sur, Universidad de La Frontera, Temuco, Chile, 2016.
Jacobianas con acción de grupo
Seminario Aritmética y Geometría, Universidad de Valparaíso, Valparaíso, Chile, 2017.
Variedades abelianas con Z_2-acción
Simposio de Investigadores Jóvenes en Dinámica y Geometría, Universidad de La Frontera, Chile, 2017.
Jacobians with group action
Seminario, Universidade Federal Fluminense, Niteroi, Río de Janeiro, Brasil, 2017.
On abelian varieties with involutions
Reunion mensual Anillo AC1415, Universidad Técnica Federico Santa María, Valparaíso, Chile, 2017.
Sobre la conexidad del lugar singular del espacio de módulos de variedades abelianas
Coloquio de Matemática, Facultad de Ciencias, Universidad de Chile, Santiago, Chile, 2017.
Superficies de Riemann determinadas por sus grupos de automorfismos
Santiago Number Theory and Algebra Seminar, Universidad de Chile, Santiago, Chile.
Superficies de Riemann compactas de género g con 4g − 4 automorfismos
Encuentro de Geometría Compleja y Dinámica Aritmética-Holomorfa, Los Angeles, Chile.
Riemann surfaces and abelian varieties with automorphisms
Emmy-Noether-Seminar, University of Erlangen-Nuremberg, Erlangen, Germany, 2019.
On Riemann surfaces and Jacobian varieties with automorphisms
Seminar of the Department of Mathematics, University of Linköping, Linköping, Sweden, 2019.
Superficies de Riemann y grupos nilpotentes
Coloquio de Matemática, Facultad de Ciencias, Universidad de Chile, Santiago, Chile, 2020 (online).
On regular non-cyclic covers of the projective line
Seminario de Geometría y Física-Matemática, Universidad Católica del Norte, Antofagasta, Chile, 2020 (online).
Grupos nilpotentes de automorfismos de superficies de Riemann
Seminario del Grupo de Geometría de la Universidad Central del Ecuador, Quito, 2021 (online).
Loci of Riemann surfaces and abelian varieties with automorphisms
Seminar, University of Linköping, Linköping, Suecia, 2022.
Automorfismos de superficies de Riemann de género p+1 donde p es primo
Santiago Number Theory and Algebra Seminar, Pontificia Universidad Católica de Chile, Santiago, 2022.
Riemann surfaces and Jacobian varieties with automorphisms
Seminario IMECC, Universidade Estadual de Campinas, Campinas, Brasil, 2022
Sobre curvas y Jacobianas con automorfismos
Coloquio del Departamento de Matemática, Facultad de Ciencias, Universidad de Chile, Santiago, Chile, 2022
Superficies de Riemann, variedades abelianas y grupos de cuaterniones generalizados
Seminario Aritmética y Geometría, UTFSM, Valparaíso, Chile, 2022.
Puntos de Weierstrass en superficies de Riemann y automorfismos
Seminario del Departamento de Matemáticas, Universidad de Concepción, Concepción, 2022.
Superficies de Riemann determinadas por sus simetrías
Coloquio del Instituto de Matemática, Universidad de Talcan, Talca, 2023
Classifying Riemann surfaces by number of symmetries
Seminar, University of Linköping, Linköping, Suecia, 2024.
Preprints
Preprints
The locus of Riemann surfaces of genus 2(p−1) with 4p automorphisms
(joint work with Angel Carocca)
Algebraic models of cyclic k-gonal curves
(joint work with Rubén A. Hidalgo)
Z_kˆm-actions of signature (0; k, ..., k)
(joint work with Rubén A. Hidalgo)
On orientably-regular maps of Euler characteristic -2p^2
(joint work with Tomás Foncea)
Docencia/Teaching
Docencia/Teaching
2026-1 Algebra Lineal
2026-2 Algebra y Geometría
2025-1 Variable compleja
2025-1 Superficies de Riemann (postgrado)
2025-2 Cuerpos y álgebras
2024-1 Teoría de grupos
2024-2 Cuerpos y álgebras
2023-1 Variable compleja
2023-1 Acciones de grupos en superficies de Riemann (postgrado)
2023-2 Grupos Kleinianos (postgrado)
2022-1 Algebra II (postgrado)
2022-2 Superficies de Riemann y curvas algebraicas
2021-1 Álgebra Lineal Avanzada (postgrado)
2021-1 Álgebra Lineal (Ingenierías Civiles)
2021-2 Matemática para la Informática II (Ingeniería Informática)
2020-1 Álgebra (Pedagogía en Matemática)
2020-2 Álgebra Lineal (Ingenierías Civiles)
2019-1 Cálculo en una variable (Ingenierías Civiles)
2019-1 Análisis I (Postgrado)
2019-2 Teoría de Números (Pedagogía en Matemática)
2019-2 Matemática Aplicada (Ingenierías Civiles)
Estudiantes/Students
Estudiantes/Students
Yazmín Rivera, Doctorado en Matemática, in progress,
Agustín Suazo, Magíster en Matemática, in progress
Tomás Foncea, Magister en Matemáticas. Tesis: "Superficies de Riemann de género 1+p^2 con 5p^2 atomorfismos". Octubre de 2025
Valentina Moreno, Magister en Matemáticas. Tesis: "Una generalización del pincel de cuárticas de Kuribayashi-Komiya". Junio de 2025
Iván Morales, Doctorado en Matemáticas. Tesis: "Familias uniparamétricas de superficies de Riemann con acción del grupo modular cíclico maximal". Octubre de 2024
Pablo Alvarado-Seguel, Magíster en Matemática, Tesis: “Representaciones de grupos de automorfismos de superficies de Riemann compactas”. Agosto de 2024
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