Displaying similar documents to “A4, A5, S4 and S5 of Schottky type.”

Schottky uniformizations of Z actions on Riemann surfaces.

Rubén A. Hidalgo (2005)

Revista Matemática Complutense

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Given a closed Riemann surface S together a group of its conformal automorphisms H ≅ Z , it is known that there are Schottky uniformizations of S realizing H. In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z as group of conformal automorphisms on a closed Riemann surface.

On soluble groups of automorphisms of nonorientable Klein surfaces

G. Gromadzki (1992)

Fundamenta Mathematicae

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We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.

Multiple prime covers of the riemann sphere

Aaron Wootton (2005)

Open Mathematics

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A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.

On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms

Ewa Tyszkowska (2003)

Open Mathematics

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The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p n are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed,...

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

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

RACSAM

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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...

Riemann and Klein surfaces with nodes viewed as quotients.

Ignacio C. Garijo (2006)

Revista Matemática Complutense

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If G is a group of automorphisms that acts properly discontinuously on a Riemann or Klein surface X, then there exists a unique structure of Riemann or Klein surface on X/G such that the projection π: X → X/G is a morphism. The analogous result is not true when we deal with surfaces with nodes. In this paper we give a new definition of a group that acts properly discontinuously on a surface with nodes in order to obtain a similar theorem.