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On real trigonal Riemann surfaces
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-9557-9566
2006 (English)In: Mathematica Scandinavica, ISSN 0025-5521, Vol. 98, no 1, 53-68 p.Article in journal (Refereed) Published
Abstract [en]

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) a 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 or is the number of connected components of the fixed point set Fix(sigma) and the orientability of the Klein surface X/(sigma). 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.

Place, publisher, year, edition, pages
2006. Vol. 98, no 1, 53-68 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-48092OAI: diva2:268988
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2015-03-09

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