Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-23T08:43:24.075Z Has data issue: false hasContentIssue false
  • English
  • Français

EQUISYMMETRIC STRATA OF THE MODULI SPACE OF CYCLIC TRIGONAL RIEMANN SURFACES OF GENUS 4

Published online by Cambridge University Press:  01 January 2009

MILAGROS IZQUIERDO  and
DANIEL YING
MILAGROS IZQUIERDO
Affiliation:
Matematiska institutionen, Linköpings universitet, 581 83 Linköping, Sweden e-mail: miizq@mai.liu.se
DANIEL YING
Affiliation:
Matematiska institutionen, Linköpings universitet, 581 83 Linköping, Sweden e-mail: dayin@mai.liu.se
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic trigonal Riemann surface. Using the characterization of cyclic trigonality by Fuchsian groups, we find the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 19 - 29
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Accola, R. D. M., On cyclic trigonal Riemann surfaces, I, Trans. Am. Math. Soc. 283 (1984), 423–449.CrossRefGoogle Scholar
2.Accola, R. D. M., A classification of trigonal Riemann surfaces, Kodai Math. J. 23 (2000), 81–87.CrossRefGoogle Scholar
3.Accola, R. D. M., On the Castelnuovo–Severi inequality for Riemann surfaces, Kodai Math. J. 29 (2006), 299–317.CrossRefGoogle Scholar
4.Broughton, A., The equisymmetric stratification of the moduli space and the Krull dimension of mapping class groups, Topol. Appl. 37 (1990), 101–113.CrossRefGoogle Scholar
5.Broughton, A., Classifying finite group actions on surfaces of low genus, J. Pure Appl. Algebra 69 (1990), 233–270.CrossRefGoogle Scholar
6.Costa, A. F. and Izquierdo, M., On real trigonal Riemann surfaces, Math. Scand. 98 (2006), 53–468.CrossRefGoogle Scholar
7.Costa, A. F., Izquierdo, M. and Ying, D., On trigonal Riemann surfaces with non-unique morphisms, Manuscr. Math. 118 (2005), 443–453.CrossRefGoogle Scholar
8.Costa, A. F., Izquierdo, M. and Ying, D., On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms, RACSAM, 101 (2007), 81–86.Google Scholar
9.Coxeter, H. S. M. and Moser, W. O. J., Generators and relations for discrete groups (Springer-Verlag, Berlin, 1957).CrossRefGoogle Scholar
10.González-Díez, G., On prime Galois covering of the Riemann sphere, Ann. Mat. Pure Appl. 168 (1995), 1–15.CrossRefGoogle Scholar
11.Harvey, W., On branch loci in Teichmüller space, Trans. Am. Math. Soc. 153 (1971), 387–399.Google Scholar
12.Nag, S., The complex analytic theory of Teichmüller spaces (Wiley-Interscience Publication, NY, 1988).Google Scholar
13.Singerman, D., Subgroups of Fuchsian groups and finite permutation groups, Bull. London Math. Soc. 2 (1970), 319–323.CrossRefGoogle Scholar
14.Singerman, D., Finitely maximal Fuchsian groups, J. Lond. Math. Soc. 6 (1972), 29–38.CrossRefGoogle Scholar
15.Wootton, A., Non-normal Belyi p-gonal surfaces. Computational aspects of algebraic curves, 95–108, Lecture Notes Ser. Comput., 13, (World Sciientific Publications, Hackensack, NJ, 2005).Google Scholar