Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2008, Article ID 609425, 18 pages
http://dx.doi.org/10.1155/2008/609425
Research Article

One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions

1Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional de Educación a Distancia (UNED), Senda del rey, 9, 28040 Madrid, Spain
2Matematiska Institutionen, Linköpings Universitet, 581 83 Linköping, Sweden
3Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile

Received 9 June 2008; Accepted 13 October 2008

Academic Editor: Heinrich Begehr

Copyright © 2008 Antonio F. Costa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Clebsch, “Zur Theorie der Riemann'schen Fläche,” Mathematische Annalen, vol. 6, no. 2, pp. 216–230, 1873. View at Google Scholar · View at MathSciNet
  2. D. Eisenbud, N. Elkies, J. Harris, and R. Speiser, “On the Hurwitz scheme and its monodromy,” Compositio Mathematica, vol. 77, no. 1, pp. 95–117, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Hurwitz, “Uber Riemann'sche Flächen mit gegebenen Verzweigungspunkten,” Mathematische Annalen, vol. 39, no. 1, pp. 1–60, 1891. View at Publisher · View at Google Scholar
  4. W. Fulton, “Hurwitz schemes and irreducibility of moduli of algebraic curves,” Annals of Mathematics, vol. 90, no. 3, pp. 542–575, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. I. I. Bouw, “Reduction of the Hurwitz space of metacyclic covers,” Duke Mathematical Journal, vol. 121, no. 1, pp. 75–111, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. I. I. Bouw and S. Wewers, “Reduction of covers and Hurwitz spaces,” Journal für die reine und angewandte Mathematik, vol. 574, pp. 1–49, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. B. Dubrovin, “Geometry of 2D topological field theories,” in Integrable Systems and Quantum Groups (Montecatini Terme, 1993), vol. 1620 of Lecture Notes in Mathematics, pp. 120–348, Springer, Berlin, Germany, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Diaz, R. Donagi, and D. Harbater, “Every curve is a Hurwitz space,” Duke Mathematical Journal, vol. 59, no. 3, pp. 737–746, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. V. Belyi, “On Galois extensions of a maximal cyclotomic field,” Mathematics of the USSR-Izvestiya, vol. 14, no. 2, pp. 247–256, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. B. Huppert, Endliche Gruppen. I, vol. 134 of Die Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 1967. View at Zentralblatt MATH
  11. G. Berger, “Fake congruence subgroups and the Hurwitz monodromy group,” Journal of Mathematical Sciences, vol. 6, no. 3, pp. 559–574, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. E. Bujalance and D. Singerman, “The symmetry type of a Riemann surface,” Proceedings of the London Mathematical Society, vol. 51, no. 3, pp. 501–519, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. Seifert and W. Threfall, A Textbook of Topology, Academic Press, New York, NY, USA, 1980.
  14. C. J. Earle, Teichmüller Spaces as Complex Manifolds, Lecture Notes, University of Warwick, Warwick, UK, 1993.
  15. E. Bujalance, “Normal N.E.C. signatures,” Illinois Journal of Mathematics, vol. 26, no. 3, pp. 519–530, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. E. Bujalance, J. J. Etayo, J. M. Gamboa, and G. Gromadzki, Automorphism Groups of Compact Bordered Klein Surfaces. A Combinatorial Approach, vol. 1439 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1990. View at Zentralblatt MATH · View at MathSciNet
  17. S. M. Natanzon, Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs, vol. 225 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 2004. View at Zentralblatt MATH · View at MathSciNet
  18. A. H. M. Hoare, “Subgroups of N.E.C. groups and finite permutation groups,” The Quarterly Journal of Mathematics, vol. 41, no. 161, pp. 45–59, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. E. Bujalance, A. F. Costa, and D. Singerman, “Application of Hoare's theorem to symmetries of Riemann surfaces,” Annales Academiae Scientiarum Fennicae. Series A I. Mathematica, vol. 18, no. 2, pp. 307–322, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet