On -hyperelliptic involutions of Riemann surfaces.
Tyszkowska, Ewa (2005)
Beiträge zur Algebra und Geometrie
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Tyszkowska, Ewa (2005)
Beiträge zur Algebra und Geometrie
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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.
Tomasz Szemberg (1991)
Annales Polonici Mathematici
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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.
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...
Grzegorz Gromadzki (2008)
Revista Matemática Complutense
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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,...
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.
Kukkurainen, Paavo (2007)
Annales Academiae Scientiarum Fennicae. Mathematica
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Singerman, David, Syddall, Robert I. (2003)
Beiträge zur Algebra und Geometrie
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Liu, Lixin, Sun, Zongliang, Wei, Hanbai (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
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Rubén A. Hidalgo (2002)
Revista Matemática Complutense
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Let H be a group of conformal automorphisms of a closed Riemann surface S, isomorphic to either of the alternating groups A or A or the symmetric groups S or S. We provide necessary and sufficient conditions for the existence of a Schottky uniformization of S for which H lifts. In particular, togheter with the previous works in Hidalgo (1994,1999), we exhaust the list of finite groups of Möbius transformations of Schottky type.
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.