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On cyclic p-gonal Riemann surfaces with several p-gonal morphisms
Departamento de Matematicas Fundamentales, UNED.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9557-9566
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2010 (English)In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 147, no 1, 139-147 p.Article in journal (Refereed) Published
Abstract [en]

Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1)2 the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p − 1)2 which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2010. Vol. 147, no 1, 139-147 p.
Keyword [en]
p-Gonal Riemann surface - Hurwitz space - Algebraic complex curve
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-52167DOI: 10.1007/s10711-009-9444-4OAI: oai:DiVA.org:liu-52167DiVA: diva2:280035
Note

The original publication is available at www.springerlink.com: Antonio F. Costa, Milagros Izquierdo and Daniel Ying, On cyclic p-gonal Riemann surfaces with several p-gonal morphisms, 2009, Geometriae Dedicata. http://dx.doi.org/10.1007/s10711-009-9444-4 Copyright: Springer Science Business Media http://www.springerlink.com/

Available from: 2009-12-08 Created: 2009-12-08 Last updated: 2017-12-12

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Izquierdo, MilagrosYing, Daniel

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