Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T07:56:49.023Z Has data issue: false hasContentIssue false

Basis of quadratic differentials for Riemann surfaces with automorphisms

Published online by Cambridge University Press:  18 May 2009

Gonzalo Riera
Affiliation:
P. Universidad Católica, Casila 306 Correo 22, Santiago, Chile, E-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

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.

The uniformization theorem says that any compact Riemann surface S of genus g≥2 can be represented as the quotient of the upper half plane by the action of a Fuchsian group A with a compact fundamental region Δ.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Klein, F., Über die transformationen 7. Ordung der elliptischen Funktionen. Mat. Ann. 25 (1885) 175196.Google Scholar
2.Kra, I., Non-variational global coordinates for Teichmüller spaces, Holomorphic Functions and Moduli II, MSRI Publications No 11 (1988) 221250.CrossRefGoogle Scholar
3.Riera, G., Deformations of Klein's curve and representations of its group of 168 automorphisms in Complex variables, theory and applications, Vol. 6 (1986) 265281.CrossRefGoogle Scholar
4.Riera, G., Automorphisms of Abelian Varieties associated with Klein Surfaces, J. London Math. Soc. (2) 51 (1995) 442452.CrossRefGoogle Scholar
5.Royden, H. L., Automorphisms and isometries of Teichmüller space in Advances in theory of Riemann surfaces (Princeton University Press, 1971).Google Scholar
6.Siegel, C. L., Topics in complex function theory, Volume II, (John Wiley 1971).Google Scholar
7.Streit, M., Homology, Belyi functions and canonical curves Ph.D. thesis, JWG Universität Frankfurt (1996).CrossRefGoogle Scholar
8.Wolpert, S., The Fenchel-Nielsen deformation, Annals of Mathematics 115 (1982), 501528.CrossRefGoogle Scholar