On branched covering of compact Riemann surfaces with automorphisms

Authors

  • Gustavo Labbé Morales Universidad de La Serena.

DOI:

https://doi.org/10.22199/S07160917.1997.0002.00004

Abstract

In this work, we give an algorithm to count the different conformal equivalence classes of compact Riemann surfaces that admit a group of automorphisms isomorphic to Z/nZ, n ? N, and that are branched coverings ofthe Riemann sphere, with signature ((n, 0); m1 ,m2 ,m3 ), m1 ,m2,m3 ? N.

By using the previous result, we count the different conformal equivalence classes of compact Riemann surfaces in the cases of coverings with signature ((p, 0); p, p, p), p ? 5 and prime, and signature ((p2, 0); p2 , p2 , p), p  ? 3 and prime.

Author Biography

Gustavo Labbé Morales, Universidad de La Serena.

Departamento de Matemáticas.

References

[1] H. Beiler, Recreation in the theory of numbers, Dover Publications, Inc., N.Y., (1966).

[2] W.J. Harvey, On branch loci in Teichmüller space, Trans. of the Amer. Math. Soc., 153, pp. 387-399, (1971)

[3] S. Lefschetz, Select Papers, Chelsea, New York, (1971).

[4] E. K. Lloyd, Riemann surface transformation groups, Journal of Combinatoria! Theory, 17-27, (1972).

[5] G. Springer, Introduction to Riemann surface, Addison-Wesley Publishing Company, Inc., (1957).

[6] C. L. Tretkoff and M. D. Tretkoff, Combinatorial group theory, Riemann surface and differential equations.

Published

2018-04-04

How to Cite

[1]
G. Labbé Morales, “On branched covering of compact Riemann surfaces with automorphisms”, Proyecciones (Antofagasta, On line), vol. 16, no. 2, pp. 141-156, Apr. 2018.

Issue

Section

Artículos