<p>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 will characterize the Riemann surfaces of genus 4 wiht non-unique trigonal morphism. We will describe the structure of the space of cyclic trigonal Riemann surfaces of genus 4.</p> / Report code: LiU-Tek-Lic-2004:54. The electronic version of the printed licentiate thesis is a corrected version where errors in the calculations have been corrected. See Errata below for a list of corrections.

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.

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 will characterize the Riemann surfaces of genus 4 wiht non-unique trigonal morphism. We will describe the structure of the space of cyclic trigonal Riemann surfaces of genus 4. / <p>Report code: LiU-Tek-Lic-2004:54. The electronic version of the printed licentiate thesis is a corrected version where errors in the calculations have been corrected. See Errata below for a list of corrections.</p>