Rubén A. Hidalgo — Geometry at the Frontier · UFRO

Researcher · UFRO

Rubén A. Hidalgo

Full Professor

Department of Mathematics and Statistics · Universidad de La Frontera

Habilitation, Universität Bielefeld, Bielefeld, Germany (1994)
Ph.D. in Mathematics, The State University of New York, Stony Brook, USA (1991)
M.A. in Sciences, mention Mathematics, Universidad Técnica Federico Santa María, Valparaíso, Chile (1987)
Bachelor's Degree in Mathematics, Universidad de Santiago de Chile, Santiago, Chile (1986)
+56 45 259 66 98
Office 210
Rubén A. Hidalgo
01
About the researcher

Biography

In August 1988, Rubén A. Hidalgo began his Ph.D. at Stony Brook University, New York, under the supervision of Bernie Maskit — thus becoming an official member of the "Maskitiers." In April 1991 he defended his thesis, focused on Schottky uniformizations of Riemann surfaces reflecting a given group of automorphisms. From 1991 he moved to Germany, specifically to Bielefeld, where he joined the SFB-343: Discrete Structures in Mathematics (1991–1993) as a Scientific Collaborator under the supervision of Professors H. Helling and J. Mennicke. In 1992 he began his Habilitation process in Bielefeld, completing his defense in early 1994. In August 1993 he took a position at Universidad Técnica Federico Santa María, in Valparaíso, Chile, a city from whose office he enjoyed a privileged view of the Pacific Ocean. In 2015, following other members of the geometry group, he joined Universidad de La Frontera, 640 kilometers south of Valparaíso — trading, as he himself describes it, the blue of the ocean for the dark green of the araucaria trees.

02
 

Research Areas

Riemann Surfaces and their Symmetries

Kleinian Groups

Holomorphic Dynamical Systems

03
Scientific output · 171 indexed publications

Publications

171 of 171 publications
2026
Article DOI

Generalized quasi-dihedral group as automorphism group of Riemann surfaces

Hidalgo, Rubén A.; Marín Montilla, Yerika L.; Quispe, Saúl

Transform. Groups Vol. 31 (2026), no. 1, 705–736.

Article DOI

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

Hidalgo, Rubén A.; Paulhus, Jennifer; Reyes-Carocca, Sebastián; Rojas, Anita M.

Transform. Groups Vol. 31 (2026), no. 1, 675–704.

Article DOI

Uniqueness of generalized Fermat groups in positive characteristic

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

Transform. Groups Vol. 31 (2026), no. 2, 1543–1556.

Article DOI

Generalized superelliptic Riemann surfaces

Hidalgo, Rubén A.; Quispe, Saúl; Shaska, Tony

Transform. Groups Vol. 31 (2026), no. 2, 1557–1569.

2025
Article

Bernard Maskit memorial tribute

Anderson, James W.; Basmajian, Ara; Hidalgo, Ruben; Susskind, Perry; Taylor, Edward C.

Notices Amer. Math. Soc. Vol. 72 (2025), no. 7, 731–739.

Article DOI

A simple observation concerning the vector of Riemann constants and non-special divisors of generalized Fermat curves

Hidalgo, Rubén A.

Cubo Vol. 27 (2025), no. 2, 209–231.

Article DOI

Explicit computation of the field of moduli of some non-hyperelliptic pseudo-real curves

Hidalgo, Rubén A.

Arch. Math. (Basel) Vol. 125 (2025), no. 1, 63–77.

Article DOI

The minima of the geodesic length functions of uniform filling curves

Girondo, Ernesto; González-Diez, Gabino; Hidalgo, Rubén A.

J. Lond. Math. Soc. (2) Vol. 111 (2025), no. 4, Paper No. e70153, 24 pp.

Article DOI

On the biggest purely non-free conformal actions on compact Riemann surfaces and their asymptotic properties

Bagiński, C.; Gromadzki, G.; Hidalgo, R. A.

J. Algebra Vol. 663 (2025), 630–651.

2024
Article DOI

Cyclic-Schottky strata of Schottky space

Hidalgo, Rubén A.; Izquierdo, Milagros

Bull. Lond. Math. Soc. Vol. 56 (2024), no. 11, 3412–3427.

Article DOI

Quasi-abelian group as automorphism group of Riemann surfaces

Hidalgo, Rubén A.; Marín Montilla, Yerika L.; Quispe, Saúl

Manuscripta Math. Vol. 175 (2024), no. 1-2, 591–616.

Article DOI

Extending finite free actions of surfaces

Hidalgo, Rubén A.

Bull. Lond. Math. Soc. Vol. 56 (2024), no. 7, 2495–2513.

Article DOI

On p-gonal fields of definition

Hidalgo, Ruben A.

Ars Math. Contemp. Vol. 24 (2024), no. 3, Paper No. 2, 10 pp.

2023
Article DOI

Structural description of dihedral extended Schottky groups and application in study of symmetries of handlebodies

Gromadzki, Grzegorz; Hidalgo, Ruben A.

Topology Appl. Vol. 339 (2023), part A, Paper No. 108568, 25 pp.

Article DOI

Quadrangular Zlp-actions on Riemann surfaces

Hidalgo, Ruben A.

Eur. J. Math. Vol. 9 (2023), no. 3, Paper No. 63, 23 pp.

Article DOI

Realising countable groups as automorphisms of origamis on the Loch Ness monster

Hidalgo, Rubén A.; Morales, Israel

Arch. Math. (Basel) Vol. 120 (2023), no. 4, 355–360.

Article DOI

Homology group automorphisms of Riemann surfaces

Hidalgo, Rubén A.

Mosc. Math. J. Vol. 23 (2023), no. 1, 113–120.

Article DOI

Smooth quotients of generalized Fermat curves

Hidalgo, Rubén A.

Rev. Mat. Complut. Vol. 36 (2023), no. 1, 27–55.

2022
Article DOI

Groups as automorphisms of dessins d'enfants

Cañas, Alejandro; Hidalgo, Rubén A.; Turiel, Francisco Javier; Viruel, Antonio

Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM Vol. 116 (2022), no. 4, Paper No. 160, 9 pp.

Article DOI

Dessins d'enfants and some holomorphic structures on the Loch Ness monster

Atarihuana, Yasmina; García, Juan; Hidalgo, Rubén A.; Quispe, Saúl; Ramírez Maluendas, Camilo

Q. J. Math. Vol. 73 (2022), no. 1, 349–367.

Book Chapter DOI

Dessins d'enfants with a given bipartite graph

Hidalgo, Ruben A.

Automorphisms of Riemann surfaces, subgroups of mapping class groups and related topics, Contemp. Math., 776, Amer. Math. Soc., [2022], pp. 249–267.

Book Chapter DOI

Fiber product of Riemann surfaces

Hidalgo, Rubén A.; Reyes-Carocca, Sebastián; Vega, Angélica A.

Automorphisms of Riemann surfaces, subgroups of mapping class groups and related topics, Contemp. Math., 776, Amer. Math. Soc., [2022], pp. 161–175.

2021
Article DOI

The structure of extended function groups

Hidalgo, R. A.

Cubo Vol. 23 (2021), no. 3, 369–384.

Article DOI

On real and pseudo-real rational maps

Hidalgo, Ruben A.; Quispe, Saúl

Nonlinearity Vol. 34 (2021), no. 9, 6248–6272.

Article DOI

Stable Riemann orbifolds of Schottky type

Díaz, Raquel; Hidalgo, Rubén A.

Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM Vol. 115 (2021), no. 3, Paper No. 111, 27 pp.

Book Chapter DOI

Weil's Galois descent theorem from a computational point of view

Hidalgo, Rubén A.; Reyes-Carocca, Sebastián

Geometry at the frontier — symmetries and moduli spaces of algebraic varieties, Contemp. Math., 766, Amer. Math. Soc., [2021], pp. 217–228.

Book Chapter DOI

Constructing Jacobian varieties with many elliptic curves

Hidalgo, Rubén A.

Geometry at the frontier — symmetries and moduli spaces of algebraic varieties, Contemp. Math., 766, Amer. Math. Soc., [2021], pp. 201–215.

Article DOI

Automorphism groups of origami curves

Hidalgo, Rubén A.

Arch. Math. (Basel) Vol. 116 (2021), no. 4, 385–390.

Article DOI

q-étale covers of cyclic p-gonal covers

Carocca, Ángel; Hidalgo, Rubén A.; Rodríguez, Rubí E.

J. Algebra Vol. 573 (2021), 393–409.

2020
Article DOI

Geometric description of virtual Schottky groups

Hidalgo, Ruben A.

Bull. Lond. Math. Soc. Vol. 52 (2020), no. 3, 530–545.

Article DOI

On n-th roots of meromorphic maps

García, Juan C.; Hidalgo, Rubén A.

Rev. Colombiana Mat. Vol. 54 (2020), no. 1, 65–74.

Article DOI

Holomorphic differentials of generalized Fermat curves

Hidalgo, Rubén A.

J. Number Theory Vol. 217 (2020), 78–101.

Article DOI

A sufficiently complicated noded Schottky group of rank three

Hidalgo, Rubén A.

Cubo Vol. 22 (2020), no. 1, 39–53.

Article DOI

A remark on the field of moduli of Riemann surfaces

Hidalgo, Rubén A.

Arch. Math. (Basel) Vol. 114 (2020), no. 5, 515–526.

Article DOI

Zapponi-orientable dessins d'enfants

Girondo, Ernesto; González-Diez, Gabino; Hidalgo, Rubén A.; Jones, Gareth A.

Rev. Mat. Iberoam. Vol. 36 (2020), no. 2, 549–570.

Article DOI

Regular dessins d'enfants with dicyclic group of automorphisms

Hidalgo, Rubén A.; Quispe, Saúl

J. Pure Appl. Algebra Vol. 224 (2020), no. 5, 106242, 9 pp.

2019
Article DOI

On the connectivity of the branch and real locus of M0,[n+1]

Atarihuana, Yasmina; Hidalgo, Rubén A.

Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM Vol. 113 (2019), no. 4, 2981–2998.

Article DOI

On square roots of meromorphic maps

García, Juan C.; Hidalgo, Rubén A.

Results Math. Vol. 74 (2019), no. 3, Paper No. 118, 12 pp.

Article DOI

On the dynamics of n-circle inversion

Hidalgo, Rubén A.; Honorato, Gerardo; Valenzuela-Henriquez, Francisco

Nonlinearity Vol. 32 (2019), no. 4, 1242–1274.

Book Chapter

An explicit descent of real algebraic varieties

Hidalgo, Rubén A.

Algebraic curves and their applications, Contemp. Math., 724, Amer. Math. Soc., [2019], pp. 235–246.

Article DOI

Weierstrass weight of the hyperosculating points of generalized Fermat curves

Hidalgo, Rubén A.; Leyton-Álvarez, Maximiliano

J. Pure Appl. Algebra Vol. 223 (2019), no. 7, 3057–3070.

Article DOI

Automorphism groups of dessins d'enfants

Hidalgo, Rubén A.

Arch. Math. (Basel) Vol. 112 (2019), no. 1, 13–18.

2018
Article

On the connectedness of the Branch locus of the Schottky space

Hidalgo, Rubén A.; Izquierdo, Milagros

Albanian J. Math. Vol. 12 (2018), no. 1, 131–136.

Article DOI

Uniformizations of stable (γ, n)-gonal Riemann surfaces

Hidalgo, Rubén A.

Anal. Math. Phys. Vol. 8 (2018), no. 4, 655–677.

Article DOI

Real structures on marked Schottky space

Hidalgo, Rubén A.; Sarmiento, Sebastián

J. Lond. Math. Soc. (2) Vol. 98 (2018), no. 2, 253–274.

Article

On Macbeath's formula for hyperbolic manifolds

Gromadzki, Grzegorz; Hidalgo, Rubén A.

Albanian J. Math. Vol. 12 (2018), no. 1, 15–23.

Article DOI

On the minimal field of definition of rational maps: rational maps of odd signature

Hidalgo, Rubén A.

Ann. Acad. Sci. Fenn. Math. Vol. 43 (2018), no. 2, 685–692.

Article DOI

p-groups acting on Riemann surfaces

Hidalgo, Rubén A.

J. Pure Appl. Algebra Vol. 222 (2018), no. 12, 4173–4188.

Book Chapter

Rational points in the moduli space of genus two

Beshaj, L.; Hidalgo, R.; Kruk, S.; Malmendier, A.; Quispe, S.; Shaska, T.

Higher genus curves in mathematical physics and arithmetic geometry, Contemp. Math., 703, Amer. Math. Soc., [2018], pp. 83–115.

Book Chapter

On the field of moduli of superelliptic curves

Hidalgo, Ruben; Shaska, Tony

Higher genus curves in mathematical physics and arithmetic geometry, Contemp. Math., 703, Amer. Math. Soc., [2018], pp. 47–62.

Article DOI

About the Fricke-Macbeath curve

Hidalgo, Ruben A.

Eur. J. Math. Vol. 4 (2018), no. 1, 313–325.

Article DOI

Riemann surfaces defined over the reals

Badr, Eslam; Hidalgo, Rubén A.; Quispe, Saúl

Arch. Math. (Basel) Vol. 110 (2018), no. 4, 351–362.

Article DOI

On the connectedness of the set of Riemann surfaces with real moduli

Costa, Antonio F.; Hidalgo, Rubén A.

Arch. Math. (Basel) Vol. 110 (2018), no. 3, 305–310.

Article DOI

A note on the connectedness of the branch locus of rational maps

Hidalgo, Ruben A.; Quispe, Saúl

Glasg. Math. J. Vol. 60 (2018), no. 1, 199–207.

2017
Article DOI

Totally degenerate extended Kleinian groups

Hidalgo, Ruben A.

Cubo Vol. 19 (2017), no. 3, 69–77.

Article DOI

Regular dessins d'enfants with field of moduli ℚ(√2)

Hidalgo, Ruben A.; Quispe, Saul

Ars Math. Contemp. Vol. 13 (2017), no. 2, 323–330.

Article DOI

On purely non-free finite actions of abelian groups on compact surfaces

Bagiński, Czesław; Gromadzki, Grzegorz; Hidalgo, Ruben A.

Arch. Math. (Basel) Vol. 109 (2017), no. 4, 311–321.

Article DOI

Quasiplatonic curves with symmetry group Z22 ⋊ Zm are definable over ℚ

Hidalgo, Rubén A.; Jiménez, Leslie; Quispe, Saúl; Reyes-Carocca, Sebastián

Bull. Lond. Math. Soc. Vol. 49 (2017), no. 1, 165–183.

Article DOI

Automorphisms of generalized Fermat curves

Hidalgo, Rubén A.; Kontogeorgis, Aristides; Leyton-Álvarez, Maximiliano; Paramantzoglou, Panagiotis

J. Pure Appl. Algebra Vol. 221 (2017), no. 9, 2312–2337.

Article DOI

A tower of Riemann surfaces which cannot be defined over their field of moduli

Artebani, Michela; Carvacho, Mariela; Hidalgo, Ruben A.; Quispe, Saúl

Glasg. Math. J. Vol. 59 (2017), no. 2, 379–393.

2016
Article DOI

Automorphisms of non-cyclic p-gonal Riemann surfaces

Costa, Antonio F.; Hidalgo, Ruben A.

Mosc. Math. J. Vol. 16 (2016), no. 4, 659–674.

Article DOI

On periodic self-homeomorphisms of closed orientable surfaces determined by their orders

Bagiński, C.; Carvacho, M.; Gromadzki, G.; Hidalgo, R.

Collect. Math. Vol. 67 (2016), no. 3, 415–429.

Article DOI

Jacobian variety of generalized Fermat curves

Carvacho, Mariela; Hidalgo, Rubén A.; Quispe, Saúl

Q. J. Math. Vol. 67 (2016), no. 2, 261–284.

Article DOI

Fields of moduli of some special curves

Hidalgo, Ruben A.; Quispe, Saúl

J. Pure Appl. Algebra Vol. 220 (2016), no. 1, 55–60.

2015
Article DOI

A remark on the decomposition of the Jacobian variety of Fermat curves of prime degree

Hidalgo, Ruben A.; Rodríguez, Rubí E.

Arch. Math. (Basel) Vol. 105 (2015), no. 4, 333–341.

Article DOI

Field of moduli of generalized Fermat curves of type (k, 3) with an application to non-hyperelliptic dessins d'enfants

Hidalgo, Ruben A.; Johnson, Pilar

J. Symbolic Comput. Vol. 71 (2015), 60–72.

Article DOI

Edmonds maps on the Fricke-Macbeath curve

Hidalgo, Rubén A.

Ars Math. Contemp. Vol. 8 (2015), no. 2, 275–289.

2014
Book Chapter

Conjugacy classes of symmetries of compact Kleinian 3-manifolds

Gromadzki, G.; Hidalgo, R. A.

Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces, Contemp. Math., 629, Amer. Math. Soc., Providence, RI, 2014, pp. 181–187.

Book Chapter

Normal coverings of hyperelliptic real Riemann surfaces

Cirre, Francisco-Javier; Hidalgo, Rubén A.

Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces, Contemp. Math., 629, Amer. Math. Soc., Providence, RI, 2014, pp. 59–75.

Article

On the connectivity of the branch locus of the Schottky space

Hidalgo, Rubén A.; Izquierdo, Milagros

Ann. Acad. Sci. Fenn. Math. Vol. 39 (2014), no. 2, 635–654.

Article

A simple remark on the field of moduli of rational maps

Hidalgo, Rubén A.

Q. J. Math. Vol. 65 (2014), no. 2, 627–635.

Article

Computing the field of moduli of the KFT family

Hidalgo, Rubén A.

Proyecciones Vol. 33 (2014), no. 1, 61–75.

2013
Article

Almost Abelian regular dessins d'enfants

Hidalgo, Ruben A.

Fund. Math. Vol. 222 (2013), no. 3, 269–278.

Article

Schottky uniformizations of symmetries

Gromadzki, G.; Hidalgo, R. A.

Glasg. Math. J. Vol. 55 (2013), no. 3, 591–613.

Article DOI

Orbifolds with signature (0; k, kn−1, kn, kn)

Carocca, Angel; Hidalgo, Rubén A.; Rodríguez, Rubí E.

Pacific J. Math. Vol. 263 (2013), no. 1, 53–85.

Article

Automorphisms group of generalized Fermat curves of type (k, 3)

Fuertes, Yolanda; González-Diez, Gabino; Hidalgo, Rubén A.; Leyton, Maximiliano

J. Pure Appl. Algebra Vol. 217 (2013), no. 10, 1791–1806.

Article

Lowest uniformizations of compact Klein surfaces

Hidalgo, Rubén A.

Rev. Mat. Iberoam. Vol. 29 (2013), no. 1, 373–379.

Article

The bipartite graphs of abelian dessins d'enfants

Hidalgo, Rubén A.

Ars Math. Contemp. Vol. 6 (2013), no. 2, 301–304.

Article

Field of moduli and generalized Fermat curves

Hidalgo, Rubén A.; Reyes-Carocca, Sebastián; Valdés, María Elisa

Rev. Colombiana Mat. Vol. 47 (2013), no. 2, 205–221.

2012
Article

Homology closed Riemann surfaces

Hidalgo, Rubén A.

Q. J. Math. Vol. 63 (2012), no. 4, 931–952.

Article

Fields of moduli of classical Humbert curves

Hidalgo, Rubén A.; Reyes, Sebastian

Q. J. Math. Vol. 63 (2012), no. 4, 919–930.

Article

A remark on (p, n)-gonal quasiplatonic Riemann surfaces

Hidalgo, Ruben A.

Geom. Dedicata Vol. 160 (2012), 309–312.

Book Chapter

Numerical Schottky uniformizations of certain cyclic L-gonal curves

Hidalgo, Rubén A.; Seppälä, Mika

Computational algebraic and analytic geometry, Contemp. Math., 572, Amer. Math. Soc., Providence, RI, 2012, pp. 97–112.

Article

On conjugacy of p-gonal automorphisms

Hidalgo, Rubén A.

Bull. Korean Math. Soc. Vol. 49 (2012), no. 2, 411–415.

Article

A simple remark on fields of definition

Hidalgo, Rubén A.

Proyecciones Vol. 31 (2012), no. 1, 25–28.

Article

Erratum: Non-hyperelliptic Riemann surfaces with real field of moduli but not definable over the reals

Hidalgo, Rubén A.

Arch. Math. (Basel) Vol. 98 (2012), no. 5, 449–451.

2011
Article

A Kleinian group version of Torelli's theorem

Hidalgo, Rubén A.

Sci. Ser. A Math. Sci. (N.S.) Vol. 21 (2011), 107–115.

Book Chapter

Numerical Schottky uniformizations: Myrberg's opening process

Hidalgo, Rubén A.; Seppälä, Mika

Computational approach to Riemann surfaces, Lecture Notes in Math., 2013, Springer, Heidelberg, 2011, pp. 195–209.

Article

Uniformization of conformal involutions on stable Riemann surfaces

Díaz, Raquel; Garijo, Ignacio; Hidalgo, Rubén A.

Israel J. Math. Vol. 186 (2011), 297–331.

Article

Conjugacy classes of automorphisms p-groups

Hidalgo, Rubén A.

Bull. Korean Math. Soc. Vol. 48 (2011), no. 4, 847–851.

Article

Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations

Hidalgo, Rubén A.

Fund. Math. Vol. 214 (2011), no. 2, 161–180.

Article

On unbranched non-normal degree four coverings of hyperelliptic Riemann surfaces

Fuertes, Yolanda; Hidalgo, Rubén A.

Q. J. Math. Vol. 62 (2011), no. 3, 593–605.

Article

The fiber product of Riemann surfaces: a Kleinian group point of view

Hidalgo, Rubén A.

Anal. Math. Phys. Vol. 1 (2011), no. 1, 37–45.

Article

On the inverse uniformization problem: real Schottky uniformizations

Hidalgo, Rubén A.

Rev. Mat. Complut. Vol. 24 (2011), no. 2, 391–420.

2010
Article

Maximal virtual Schottky groups: explicit constructions

Hidalgo, Rubén A.

Rev. Colombiana Mat. Vol. 44 (2010), no. 1, 41–57.

Article

A short note on M-symmetric hyperelliptic Riemann surfaces

Hidalgo, Rubén A.

Cubo Vol. 12 (2010), no. 1, 175–179.

Article

Navier-Stokes equations on weighted graphs

Hidalgo, Rubén A.; Godoy Molina, Mauricio

Complex Anal. Oper. Theory Vol. 4 (2010), no. 3, 525–540.

Article

Lowest uniformizations of closed Riemann orbifolds

Hidalgo, Rubén A.

Rev. Mat. Iberoam. Vol. 26 (2010), no. 2, 639–649.

Article

Structure of Whittaker groups and applications to conformal involutions on handlebodies

Díaz, R.; Garijo, I.; Gromadzki, G.; Hidalgo, R. A.

Topology Appl. Vol. 157 (2010), no. 15, 2347–2361.

Book Chapter

A note on the lifting of automorphisms

Hidalgo, Rubén A.; Maskit, Bernard

Geometry of Riemann surfaces, London Math. Soc. Lecture Note Ser., 368, Cambridge Univ. Press, 2010, pp. 260–267.

Article

Geometric orbifolds with a torsion-free derived group

Idal'go, R. A. [Hidalgo, Rubén A.]; Mednykh, A. D.

Sib. Math. J. Vol. 51 (2010), no. 1, 38–47.

Article

Maximal Schottky extension groups

Hidalgo, Rubén A.

Geom. Dedicata Vol. 146 (2010), 141–158.

Article

Schottky double covers

Hidalgo, Rubén A.

Rev. Mat. Complut. Vol. 23 (2010), no. 1, 37–48.

Article

Fixed points of imaginary reflections on hyperbolic handlebodies

Hidalgo, Rubén A.; Maskit, Bernard

Math. Proc. Cambridge Philos. Soc. Vol. 148 (2010), no. 1, 135–158.

2009
Book Chapter

A theoretical algorithm to get a Schottky uniformization from a Fuchsian one

Hidalgo, Rubén A.

Analysis and mathematical physics, Trends Math., Birkhäuser, Basel, 2009, pp. 193–204.

Article

Non-hyperelliptic Riemann surfaces with real field of moduli but not definable over the reals

Hidalgo, Rubén A.

Arch. Math. (Basel) Vol. 93 (2009), no. 3, 219–224.

Article

Generalized Fermat curves

González-Diez, Gabino; Hidalgo, Rubén A.; Leyton, Maximiliano

J. Algebra Vol. 321 (2009), no. 6, 1643–1660.

2008
Article

Existence of solutions of semilinear systems in l²

Hidalgo, Rubén; Godoy, Mauricio

Proyecciones Vol. 27 (2008), no. 2, 171–183.

Article

Zeros of semilinear systems with applications to nonlinear partial difference equations on graphs

Hidalgo, Rubén A.

J. Difference Equ. Appl. Vol. 14 (2008), no. 9, 953–969.

Article

On the retrosection theorem

Hidalgo, Rubén

Proyecciones Vol. 27 (2008), no. 1, 29–61.

Article

Generalized Humbert curves

Carocca, Angel; González-Aguilera, Víctor; Hidalgo, Rubén A.; Rodríguez, Rubí E.

Israel J. Math. Vol. 164 (2008), 165–192.

2007
Article

On uniqueness of automorphisms groups of Riemann surfaces

Leyton A., Maximiliano; Hidalgo, Rubén A.

Rev. Mat. Iberoam. Vol. 23 (2007), no. 3, 793–810.

Article

Classical Schottky uniformizations of genus 2: a package for MATHEMATICA

Hidalgo, Rubén A.

Sci. Ser. A Math. Sci. (N.S.) Vol. 15 (2007), 67–94.

Article

Finite dimensional grading of the Virasoro algebra

Hidalgo, Rubén A.; Markina, Irina; Vasil'ev, Alexander

Georgian Math. J. Vol. 14 (2007), no. 3, 419–434.

Article

On q-n-gonal Klein surfaces

Estrada, B.; Hidalgo, R. A.; Martínez, E.

Acta Math. Sin. (Engl. Ser.) Vol. 23 (2007), no. 10, 1833–1844.

2006
Article

Noded Teichmüller spaces

Hidalgo, Rubén A.; Vasil'ev, Alexander

J. Anal. Math. Vol. 99 (2006), 89–107.

Article

On neoclassical Schottky groups

Hidalgo, Rubén; Maskit, Bernard

Trans. Amer. Math. Soc. Vol. 358 (2006), no. 11, 4765–4792.

Book Chapter

Lowest uniformizations of compact real surfaces

Hidalgo, Rubén A.; Maskit, Bernard

The geometry of Riemann surfaces and abelian varieties, Contemp. Math., 397, Amer. Math. Soc., Providence, RI, 2006, pp. 145–152.

2005
Article

On Klein-Schottky groups

Hidalgo, Rubén A.; Maskit, Bernard

Pacific J. Math. Vol. 220 (2005), no. 2, 313–328.

Article

Torsion free commutator subgroups of generalized Coxeter groups

Hidalgo, Rubén A.; Rosenberger, Gerhard

Results Math. Vol. 48 (2005), no. 1-2, 50–64.

Article

Schottky uniformizations of Z22 actions on Riemann surfaces

Hidalgo, Rubén A.

Rev. Mat. Complut. Vol. 18 (2005), no. 2, 427–453.

Article

Numerical Schottky uniformizations

Hidalgo, Rubén A.; Figueroa, Jaime

Geom. Dedicata Vol. 111 (2005), 125–157.

Article

Real Schottky parametrizations

Hidalgo, Rubén A.

Complex Var. Theory Appl. Vol. 50 (2005), no. 6, 401–426.

Article

Schottky uniformizations of genus 3 and 4 reflecting S4

Hidalgo, Rubén A.

J. London Math. Soc. (2) Vol. 72 (2005), no. 1, 185–204.

Article

Automorphism groups of Schottky type

Hidalgo, Rubén A.

Ann. Acad. Sci. Fenn. Math. Vol. 30 (2005), no. 1, 183–204.

2004
Article

Abelian automorphisms groups of Schottky type

Hidalgo, Rubén A.

Proyecciones Vol. 23 (2004), no. 3, 187–203.

Article

A Schottky description of a theorem of Conder-Maclahlan-Vasiljevic-Wilson

Hidalgo, Rubén A.

Sci. Ser. A Math. Sci. (N.S.) Vol. 10 (2004), 53–63.

Article

Maximal real Schottky groups

Hidalgo, Rubén A.

Rev. Mat. Iberoamericana Vol. 20 (2004), no. 3, 737–770.

Article

Real Schottky uniformizations and Jacobians of May surfaces

Hidalgo, Rubén A.; Rodríguez, Rubí E.

Rev. Mat. Iberoamericana Vol. 20 (2004), no. 3, 627–646.

Article

Cyclic extensions of Schottky uniformizations

Hidalgo, Rubén A.

Ann. Acad. Sci. Fenn. Math. Vol. 29 (2004), no. 2, 329–344.

Article

Schottky uniformizations of genus 6 Riemann surfaces admitting A5 as group of automorphisms

Hidalgo, Rubén A.; González-A, Víctor; Labbe, Gustavo

Geom. Dedicata Vol. 106 (2004), 79–95.

2003
Article

Fixed point parameters for Fuchsian groups of type (1, 2, 0)

Hidalgo, Rubén A.

Sci. Ser. A Math. Sci. (N.S.) Vol. 6 (1994/00), 97–110 (2003).

Article

A commutator rigidity for function groups and Torelli's theorem

Hidalgo, Rubén A.

Proyecciones Vol. 22 (2003), no. 2, 117–125.

Article

Hyperbolic polygons and real Schottky groups

Hidalgo, Rubén A.

Complex Var. Theory Appl. Vol. 48 (2003), no. 1, 43–62.

2002
Book Chapter

Real surfaces, Riemann matrices and algebraic curves

Hidalgo, Rubén A.

Complex manifolds and hyperbolic geometry (Guanajuato, 2001), Contemp. Math., 311, Amer. Math. Soc., Providence, RI, 2002, pp. 277–299.

Article

Harmonic moduli of families of curves on Teichmüller spaces

Vasil'ev, Alexander; Hidalgo, Rubén

Sci. Ser. A Math. Sci. (N.S.) Vol. 8 (2002), 63–73.

Article

A4, A5, S4 and S5 of Schottky type

Hidalgo, Rubén A.

Rev. Mat. Complut. Vol. 15 (2002), no. 1, 11–29.

Article

Some special Kleinian groups and their orbifolds

Hidalgo, Rubén

Proyecciones Vol. 21 (2002), no. 1, 21–50.

2001
Article

Γ-hyperelliptic-symmetric Schottky groups

Hidalgo, Rubén A.

Complex Variables Theory Appl. Vol. 45 (2001), no. 2, 117–141.

Article

Schottky uniformization of stable symmetric Riemann surfaces

Hidalgo, Rubén A.

Notas Soc. Mat. Chile (N.S.) No. 1 (2001), 82–91.

Article

Fixed point parameters for Fuchsian groups of signature (2, 0)

Hidalgo, Rubén A.

Notas Soc. Mat. Chile (N.S.) No. 1 (2001), 11–21.

Article

Schottky uniformizations and Riemann matrices of maximal symmetric Riemann surfaces of genus 5

Hidalgo, Rubén

Proyecciones Vol. 20 (2001), no. 1, 93–126.

Article

Numerical uniformization of hyperelliptic-M-symmetric Riemann surfaces

Hidalgo, Rubén

Proyecciones Vol. 20 (2001), no. 3, 351–365.

Article

Bounds for conformal automorphisms of Riemann surfaces with condition (A)

Hidalgo, Rubén A.

Proyecciones Vol. 20 (2001), no. 2, 139–175.

Article

Anticonformal automorphisms and Schottky coverings

Hidalgo, Rubén A.; Costa, Antonio F.

Ann. Acad. Sci. Fenn. Math. Vol. 26 (2001), no. 2, 489–508.

2000
Article

A note on the homology covering of analytically finite Klein surfaces

Hidalgo, Rubén A.

Complex Variables Theory Appl. Vol. 42 (2000), no. 2, 183–192.

Article

Fixed point parameters for Möbius groups

Hidalgo, Rubén A.

Proyecciones Vol. 19 (2000), no. 2, 157–196.

Article

Fixed points parameters for Teichmüller space of closed Riemann surfaces

Hidalgo, Rubén A.; Labbé, Gustavo

Proyecciones Vol. 19 (2000), no. 1, 65–94.

1999
Article

Corrigenda: 'Some generalized Coxeter groups and their orbifolds'

Hagelberg, Marcel; Hidalgo, Rubén A.

Rev. Mat. Iberoamericana Vol. 15 (1999), no. 3, 635.

Article

A note on the homology covering of closed Klein surfaces

Hidalgo, Rubén

Proyecciones Vol. 18 (1999), no. 2, 165–173.

Book Chapter

Noded function groups

Hidalgo, Rubén A.

Complex geometry of groups (Olmué, 1998), Contemp. Math., 240, Amer. Math. Soc., Providence, RI, 1999, pp. 209–222.

Article

Dihedral groups are of Schottky type

Hidalgo, Rubén A.

Proyecciones Vol. 18 (1999), no. 1, 23–48.

Article

Cyclic groups of automorphisms of Schottky type

Hidalgo, Rubén A.

Proyecciones Vol. 18 (1999), no. 1, 13–21.

1998
Article

γ-hyperelliptic Riemann surfaces

Hidalgo, Rubén A.

Proyecciones Vol. 17 (1998), no. 1, 77–117.

Article

Noded Fuchsian groups. I

Hidalgo, Rubén A.

Complex Variables Theory Appl. Vol. 36 (1998), no. 1, 45–66.

Article

On a theorem of Accola

Hidalgo, Rubén A.

Complex Variables Theory Appl. Vol. 36 (1998), no. 1, 19–26.

Article

An example of degeneration on the noded Schottky space

Hidalgo, Rubén A.

Rev. Mat. Complut. Vol. 11 (1998), no. 1, 165–183.

1997
Article

Some generalized Coxeter groups and their orbifolds

Hagelberg, Marcel; Hidalgo, Rubén A.

Rev. Mat. Iberoamericana Vol. 13 (1997), no. 3, 543–566.

Article

Conformal versus topological conjugacy of automorphisms on compact Riemann surfaces

González-Diez, Gabino; Hidalgo, Rubén A.

Bull. London Math. Soc. Vol. 29 (1997), no. 3, 280–284.

1996
Article

Closed Riemann surfaces with dihedral groups of conformal automorphisms

Hidalgo, Rubén A.

Proyecciones Vol. 15 (1996), no. 1, 47–90.

Article

The noded Schottky space

Hidalgo, Rubén A.

Proc. London Math. Soc. (3) Vol. 73 (1996), no. 2, 385–403.

Article

A note on the 12(g − 1) bound

Hidalgo, Rubén A.

C. R. Math. Rep. Acad. Sci. Canada Vol. 18 (1996), no. 1, 39–42.

1995
Article

Kleinian groups with common commutator subgroup

Hidalgo, Rubén A.

Complex Variables Theory Appl. Vol. 28 (1995), no. 2, 121–133.

Article

A commutator rigidity for Kleinian groups

Hidalgo, Rubén A.

Proyecciones Vol. 14 (1995), no. 2, 75–81.

Article

Kleinian groups with an invariant Jordan curve: J-groups

Hidalgo, Rubén A.

Pacific J. Math. Vol. 169 (1995), no. 2, 291–310.

Article

On simultaneous homomorphisms onto Kleinian groups

Hidalgo, Rubén; Pommerenke, Ch.

Complex Variables Theory Appl. Vol. 27 (1995), no. 4, 309–315.

1994
Article

On Schottky groups with automorphisms

Hidalgo, Rubén A.

Ann. Acad. Sci. Fenn. Ser. A I Math. Vol. 19 (1994), no. 2, 259–289.

Article

The mixed elliptically fixed point property for Kleinian groups

Hidalgo, Rubén A.

Ann. Acad. Sci. Fenn. Ser. A I Math. Vol. 19 (1994), no. 2, 247–258.

Article

Schottky uniformizations of closed Riemann surfaces with abelian groups of conformal automorphisms

Hidalgo, Rubén A.

Glasgow Math. J. Vol. 36 (1994), no. 1, 17–32.

1993
Article

Homology coverings of Riemann surfaces

Hidalgo, Rubén A.

Tohoku Math. J. (2) Vol. 45 (1993), no. 4, 499–503.

1989
Article

On τ-hyperelliptic Schottky groups

Hidalgo, Rubén

Notas Soc. Mat. Chile Vol. 8 (1989), no. 1, 27–36.

04
Funding

Awarded Grants

FONDECYT Regular · 1230001

A Rigidity Property of Kleinian Groups

Principal Investigator: Rubén A. Hidalgo
Funding: National Fund for Scientific and Technological Development (FONDECYT) Regular · ANID
Period: April 2023 – March 2027

Ongoing

REDES · 190145

Joint USA-CHILE Geometry at the Frontier

Principal Investigator: Rubén A. Hidalgo
Funding: ANID · REDES
Period: 2019 – 2022

Completed

FONDECYT Regular · 1190001

Riemann Surfaces, Dessins d'Enfants and Origamis

Principal Investigator: Rubén A. Hidalgo
Funding: National Fund for Scientific and Technological Development (FONDECYT) Regular · ANID
Period: April 2019 – March 2023

Completed

FONDECYT Regular · 1150003

Riemann Surfaces, Fields of Definition and Field of Moduli

Principal Investigator: Rubén A. Hidalgo
Funding: National Fund for Scientific and Technological Development (FONDECYT) Regular · ANID
Period: March 2015 – March 2019

Completed
05
Science and community

Outreach & Engagement

This section is under construction.
Outreach and engagement activity information will be added soon.

06
Training future researchers

Graduate Supervision

Graduated Students

2025

Henry Hughes Villarroel

Advisor

Ph.D. in Sciences, mention Mathematics · Universidad de La Frontera, Temuco, Chile

Thesis: Generalized Fermat varieties in arbitrary characteristic

2024

Yerika Marín Montilla

Co-advisor

Ph.D. in Sciences, mention Mathematics · Universidad de La Frontera, Temuco, Chile

Thesis: Generalized quasi-Dihedral and quasi-Abelian groups actions on Riemann/Klein surfaces

2019

Yasmina Atarihuana

Advisor

Ph.D. in Sciences, mention Mathematics · Universidad de La Frontera, Temuco, Chile

Thesis: On the Connectivity of the Branch and Real Locus of M0,[n+1]

2019

Juan Carlos García

Advisor

Ph.D. in Sciences, mention Mathematics · Universidad de La Frontera, Temuco, Chile

Thesis: A Remark on Z-orientability of Kleinian Groups

2017

Sebastián Sarmiento

Advisor

Ph.D. in Mathematics · Universidad Técnica Federico Santa María, Valparaíso, Chile

Thesis: Real Structures on Marked Schottky Spaces

2017

Angélica Vega Moreno

Advisor

Ph.D. in Sciences, mention Mathematics · Universidad de Chile, Santiago, Chile

Thesis: Riemann Surfaces and their Dessins d'Enfants