On Riemann surfaces with non-unique cyclic trigonal morphism. (English) Zbl 1137.30013

A closed Riemann surface 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. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called cyclic trigonal Riemann surface. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus greater or equal to 5. Using the characterization of cyclic trigonality by Fuchsian groups given by the first two authors [Math. Scand. 98, No. 1, 53–68 (2006; Zbl 1138.30023)], we obtain the Riemann surfaces of low genus with non-unique trigonal morphisms.


30F20 Classification theory of Riemann surfaces
30F15 Harmonic functions on Riemann surfaces
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)


Zbl 1138.30023
Full Text: DOI


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