Biblioteca de la Universidad Complutense de Madrid

Automorphism groups of hyperelliptic Riemann surfaces

Impacto

Bujalance, E. y Etayo Gordejuela, J. Javier (1987) Automorphism groups of hyperelliptic Riemann surfaces. Kodai Mathematical Journal, 10 (2). pp. 174-181. ISSN 0386-5991

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

604kB

URL Oficial: http://projecteuclid.org/euclid.kmj/1138037412




Resumen

If G is a group of automorphisms of a hyperelliptic Riemann surface of genus g represented as D/$\Gamma$ where D is the hyperbolic plane and $\Gamma$ a Fuchsian group, then $G\cong \Gamma '/\Gamma$ where $\Gamma$ ' is also a Fuchsian group. Furthermore G contains a central subgroup $G\sb 1$ of order 2 and if $\Gamma\sb 1$ is the corresponding subgroup of $\Gamma$ ', then $G/G\sb 1$ is a group of automorphisms of the sphere $D/\Gamma\sb 1$. Using this and structure theorem for Fuchsian groups the authors determine all surfaces of genus $g>3$ admitting groups G with $o(G)>8(g-1)$. There are two infinite families both corresponding to $\Gamma$ ' being the triangle group (2,4,m) and six other groups.


Tipo de documento:Artículo
Palabras clave:Classification theory of Riemann surfaces; Coverings, fundamental group; Special curves and curves of low genus
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:15765
Referencias:

COXETER, H. S. M., AND MOSER, W. O. J., "Generators and relations for discrete groups". Ergeb. der Math., 14. Springer. Berlin, etc. 1980 (4th ed.).

HARVEY, W. J., "On branch loci in Teichmuller space". Trans. Amer. Math. Soc 153 (1971), 387-399.

HURWITZ, A., "Uber algebraische Gebilde mit eindeutigen Transformationen i sich". Math. Ann. 41 (1893), 403-442.

KURIBAYASHI, A., "On analytic families of compact Riemann surfaces with non trivial automorphisms". Nagoya Math. J. 28 (1966), 119-165.

KURIBAYASHI, I., "Hyperelliptic AM curves of genus three and associated representations". Preprint.

MACBEATH, A. M., "Discontinuous groups and birational transformations". Proc Dundee Summer School 1961, 59-75.

MACLACHLAN, C., "A bound for the number of automorphisms of a compact Riemann surface".J. London Math. Soc. 44 (1969), 265-272.

MACLACHLAN, C., Maximal normal Fuchsian groups. 111. J. Math. 15 (1971), 104 113.

MACLACHLAN, C., Smooth coverings of hyperelliptic surfaces. Quart. J. Math Oxford. (2) 22(1971), 117-123.

SINGERMAN, D., Symmetries of Riemann surfaces with large automorphism group Math. Ann. 210 (1974), 17-32.

SINGERMAN, D., Symmetries and pseudo-symmetries of hyperelliptic ^surf aces Glasgow Math. J. 21 (1980), 39-49.

WIMAN, A., Uber die hypereiptischen Curven und diejenigen vom^Geschecht p=3, welche eindeutigen Transformationen in sich zulassen, Bihang Kongl. Svenska Vetenskapsakademiens Handlingar, Stockholm 1895-96.

Depositado:26 Jun 2012 10:34
Última Modificación:06 Feb 2014 10:31

Sólo personal del repositorio: página de control del artículo