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

- 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:**

- Families of Riemann surfaces, uniformization and arithmeticity (with S. Reyes-Caroccal). Trans. A.M.S (2016?)
- 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
**P**¹, 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 H
_{2}(M_{g}), Proc. Amer. Math. Soc. 113 (1991), no. 2, 335-344.

**Preprints:**

- Arbitrarily large Galois orbits of non-homeomorphic surfaces (with G. A. Jones and D. Torres-Teigell), arXiv:1110.4930.