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On the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2006 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis characterizes the cyclic trigonal Riemann surfaces of genus 4 with non-unique trigonal morphism using the automorphism groups of the surfaces. The thesis shows that Accola’s bound is sharp with the existence of a uniparametric family of cyclic trigonal Riemann surfaces of genus 4 having several trigonal morphisms. The structure of the moduli space of trigonal Riemann surfaces of genus 4 is also characterized.

Finally, by using the same technique as in the case of cyclic trigonal Riemann surfaces of genus 4, we are able to deal with p-gonal Riemann surfaces and show that Accola’s bound is sharp for p-gonal Riemann surfaces. Furthermore, we study families of p-gonal Riemann surfaces of genus (p − 1)2 with two p-gonal morphisms, and describe the structure of their moduli space.

Place, publisher, year, edition, pages
Matematiska institutionen , 2006. , 123 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1060
Keyword [en]
Riemann surface, Riemann sphere, Trigonal morphism
National Category
URN: urn:nbn:se:liu:diva-8237ISBN: 91-85643-38-6OAI: diva2:23078
Public defence
2006-12-14, Nobel, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2015-03-09

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Ying, Daniel
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