On the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4
2006 (English)Doctoral thesis, monograph (Other academic)
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
Riemann surface, Riemann sphere, Trigonal morphism
IdentifiersURN: urn:nbn:se:liu:diva-8237ISBN: 91-85643-38-6OAI: oai:DiVA.org:liu-8237DiVA: diva2:23078
2006-12-14, Nobel, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Singerman, David, Professor