Web page of the reseach group of the Universidad Autónoma of Madrid on compact Riemann surfaces.

Books:

• Introduction to compact Riemann surfaces and dessins d'enfants
  E. Girondo, G. González-Diez
  London Mathematical Society Student Texts, 79
  Cambridge University Press, Cambridge, 2012. xii+298 pp.
  ISBN: 978-0-521-74022-7
• Geometry of Riemann surfaces
  Editors: F. P. Gardiner, G. González-Diez, C. Kourouniotis
  London Mathematical Society Lecture Note Series, 368
  Cambridge University Press, Cambridge, 2010. xx+395 pp.
  ISBN: 978-0-521-73307-6

Publications:

• Galois action on Fuchsian surface groups and their associated solenoids.(with A. Dzambic). Forum Math (to appear) https://doi.org/10.1515/forum-2020-0148
• Galois action on universal covers of Kodaira surfaces. Duke Math. J, 169 (2020) no. 7 (2020) 1281-1303. https://projecteuclid.org/euclid.dmj/1585188223
• Zapponi-orientable dessins d'enfants (with E. Girondo, R. Hidalgo and G. Jones). Revista Matemática Iberoamericana (to appear)
• Arbitrary large Galois orbits of non-homeomorphic surfaces (with G. A. Jones and D. Torres-Teigell); a modified version published in European Journal of Mathematics. 4 (2018) 223–241.
• Families of Riemann surfaces, uniformization and arithmeticity (with S. Reyes-Caroccal). Trans. A.M.S, 370 (2018), 1529--1549
• The absolute Galois group acts faithfully on regular dessins and on Beauville surfaces (with Andrei Jaikin-Zapirain); a shorter version published in Proc. London Math. Soc. (2015) 111 (4): 775-796. doi: 10.1112/plms/pdv041.
• The arithmeticity of a Kodaira fibration is determined by its universal cover (with S. Reyes-Carocca), Comment. Math. Helv. 90 (2015), no. 2, 429–434
• Beauville surfaces with abelian Beauville group (with G. A. Jones and D. Torres-Teigell), Math. Scand.114 (2014), no. 2, 191–204.
• Automorphisms group of generalized Fermat curves of type (k,3) (with Y. Fuertes, R. Hidalgo and M.Leyton), J. Pure Appl. Algebra. 217 (2013), no. 10, 1791–1806
• Non-homeomorphic Galois conjugate Beauville structures on PSL(2,p) (with D. Torres-Teigell), Adv. Math. 229 (2012), no. 6, 3096–3122.
• An introduction to Beauville surfaces via uniformization (with D. Torres-Teigell), in Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces, Contemporary Mathematics, 575 (2012), 123-151.
• Z_N-Curves Possessing No Thomae Formulae of Bershadsky–Radul Type (with D. Torres-Teigell), Lett. Math. Phys. 98 (2011), no. 2, 193-205.
• On Beauville surfaces (with Y. Fuertes and A. Jaikin-Zapirain), Groups Geom. Dyn. 5 (2011), no. 1, 107-119.
• On complex curves and complex surfaces defined over number fields (with E. Girondo), in Teichmüller theory and moduli problem, Ramanujan Math. Soc. Lect. Notes Ser. 10 (2010), 247-280.
• On Beauville structures on the groups S_n and A_n (with Y. Fuertes), Math. Z. 264 (2010), no. 4, 959-968.
• Non-special divisors supported on the branch set of a p-gonal Riemann surface, in Geometry of Riemann surfaces, London Math. Soc. Lecture Note Ser. 368 (2010), 238-259.
• Right triangles with algebraic sides and elliptic curves over number fields (with E. Girondo, E. González-Jiménez, R. Steuding and J. Steuding), Math. Slovaca 59 (2009), no. 3, 299-306.
• Generalized Fermat Curves (with R. Hidalgo and M. Leyton), J. Algebra 321 (2009), no. 6, 1643-1660.
• Belyi's theorem for complex surfaces, Amer. J. Math. 130 (2008), no. 1, 59-74.
• On unramified normal coverings of hyperelliptic curves (with Y. Fuertes), J. Pure Appl. Algebra 208 (2007), no. 3, 1063-1070.
• A note on the action of the absolute Galois group on dessins (with E. Girondo), Bull. Lond. Math. Soc. 39 (2007), no. 5, 721-723.
• Smooth double coverings of hyperelliptic curves (with Y. Fuertes), in The geometry of Riemann surfaces and abelian varieties, Contemp. Math., 397 (2006), 73-77.
• Fields of moduli and definition of hyperelliptic covers (with Y. Fuertes), Arch. Math. (Basel) 86 (2006), no. 5, 398-408. (Corrigendum)
• Variations on Belyi's theorem, Q. J. Math. 57 (2006), no. 3, 339-354.
• On the structure of the Whittaker sublocus of moduli space of algebraic curves (with E. Girondo), Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), no. 2, 337-346.
• On a conjecture of Whittaker concerning uniformization of hyperelliptic surfaces (with E. Girondo), Trans. Amer. Math. Soc. 356 (2004), no. 2, 691-702.
• A Fuchsian group proof of the hyperellipticity of Riemann surfaces of genus 2 (with Y. Fuertes), Ann. Acad. Sci. Fenn. Math. 28 (2003), no. 1, 69-74.
• On extremal Riemann surfaces and their uniformizing Fuchsian groups (with E. Girondo), Glasg. Math. J. 44 (2002), no. 1, 149-157.
• Genus two extremal surfaces: extremal discs, isometries and Weierstrass points (with E. Girondo), Israel J. Math. 132 (2002), 221-238.
• On families of algebraic curves with automorphisms (with W. J. Harvey), in Complex manifolds and hyperbolic geometry, Contemp. Math. 311 (2002), 261-276.
• On the fundamental groups at infinity of the moduli spaces of compact Riemann surfaces (with P. Lochak), Michigan Math. J. 49 (2001), no. 3, 493-500.
• On extremal discs inside compact hyperbolic surfaces (with E.Girondo), C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 1, 57-60.
• Surface groups inside mapping class groups (with W. J. Harvey), Topology 38 (1999), no. 1, 57-69.
• Subvarieties of moduli space for Riemann surfaces (with W. J. Harvey), in Complex geometry of groups, Contemp. Math. 240 (1999), 197–208.
• Conformal versus topological conjugacy of automorphisms on compact Riemann surfaces (with R. Hidalgo), Bull. London Math. Soc. 29 (1997), no. 3, 280-284.
• On the Lefschetz number of quasiconformal mappings of compact Riemann surfaces (with Y. Fuertes), J. London Math. Soc. (2) 56 (1997), no. 3, 567-578.
• On prime Galois coverings of the Riemann sphere, Ann. Mat. Pura Appl. (4) 168 (1995), 1-15.
• On the number of coincidences of morphisms between closed Riemann surfaces (with Y. Fuertes), Publ. Mat. 37 (1993), no. 2, 339-353.
• Theta functions on the boundary of moduli space, in Curves, Jacobians, and abelian varieties, Contemp. Math. 136 (1992), 185-208.
• Moduli of Riemann Surfaces with Symmetry (with W. J. Harvey), in Discrete groups and geometry, London Math. Soc. Lecture Note Ser. 173 (1992), 75-93.
• Loci of curves which are prime Galois Coverings of P¹, Proc. London Math. Soc. (3) 62 (1991), no. 3, 469-489.
• On complete curves in moduli space II (with W. Harvey), Math. Proc. Cambridge Philos. Soc. 110 (1991), no. 3, 467-472.
• On complete curves in moduli space I (with W. Harvey), Math. Proc. Cambridge Philos. Soc. 110 (1991), no. 3, 461-466.
• On a basis for H₂(M_g), Proc. Amer. Math. Soc. 113 (1991), no. 2, 335-344.

Preprints:

• Complex surfaces with mutually non-biholomorphic covers (with S. Reyes-Caroccal).