On real trigonal Riemann surfaces
- Autores: A. F. Costa, M. Izquierdo
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 98, Nº 1, 2006, págs. 53-68
- Idioma: inglés
- Enlaces
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Resumen
A closed Riemann surface X which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. A trigonal Riemann surface X is called real trigonal if there is an anticonformal involution (symmetry) σ of X commuting with the trigonal morphism. If the trigonal morphism is a cyclic regular covering the Riemann surface is called real cyclic trigonal. The species of the symmetry σ is the number of connected components of the fixed point set Fix(σ) and the orientability of the Klein surface X/⟨σ⟩. We characterize real trigonality by means of Fuchsian and NEC groups. Using this approach we obtain all possible species for the symmetry of real cyclic trigonal and real non-cyclic trigonal Riemann surfaces.
