Displaying similar documents to “Theory of coverings in the study of Riemann surfaces”

Basis of homology adapted to the trigonal automorphism of a Riemann surface.

Helena B. Campos (2007)

RACSAM

Similarity:

A closed (compact without boundary) Riemann surface S of genus g is said to be trigonal if there is a three sheeted covering (a trigonal morphism) from S to the Riemann sphere, ƒ : S →Ĉ. If there is an automorphism of period three, φ, on S permuting the sheets of the covering, we shall call S cyclic trigonal and will be called trigonal automorphism. In this paper we determine the intersection matrix on the first homology group of a cyclic trigonal Riemann surface on an adapted basis...

Conformal actions with prescribed periods on Riemann surfaces

G. Gromadzki, W. Marzantowicz (2011)

Fundamenta Mathematicae

Similarity:

It is a natural question what is the set of minimal periods of a holomorphic maps on a Riemann surface of negative Euler characteristic. Sierakowski studied ordinary holomorphic periods on classical Riemann surfaces. Here we study orientation reversing automorphisms acting on classical Riemann surfaces, and also automorphisms of non-orientable unbordered Klein surfaces to which, following Singerman, we shall refer to as non-orientable Riemann surfaces. We get a complete set of conditions...

On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.

Antonio F. Costa, Milagros Izquierdo, Daniel Ying (2007)

RACSAM

Similarity:

A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space...

Automorphisms of Riemann surfaces with two fixed points

Tomasz Szemberg (1991)

Annales Polonici Mathematici

Similarity:

We give an upper bound for the order of an automorphism of a Riemann surface with two fixed points. The main results are presented in Theorems 1.4 and 2.4.