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On Riemann surfaces with non-unique cyclic trigonal morphism

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Abstract

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 in [3], we obtain the Riemann surfaces of low genus with non-unique trigonal morphisms.

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Authors and Affiliations

  1. Depto. de Matemáticas Fundamentales, UNED, C/Senda del Rey 9, 28040, Madrid, Spain

    Antonio F. Costa

  2. Matematiska Institutionen, Linköpings Universitet, 581 83, Linköping, Sweden

    Milagros Izquierdo & Daniel Ying

Authors
  1. Antonio F. Costa
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  2. Milagros Izquierdo
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  3. Daniel Ying
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Correspondence to Antonio F. Costa.

Additional information

Partially supported by BFM2002-4801.

Partially supported by the Swedish Research Council (VR)

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Costa, A., Izquierdo, M. & Ying, D. On Riemann surfaces with non-unique cyclic trigonal morphism. manuscripta math. 118, 443–453 (2005). https://doi.org/10.1007/s00229-005-0593-y

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  • DOI: https://doi.org/10.1007/s00229-005-0593-y

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