Cyclic extensions of Schottky uniformizations.

Hidalgo, Rubén A.

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Displaying similar documents to “Cyclic extensions of Schottky uniformizations.”

Automorphism groups of Schottky type.

Hidalgo, Rubén A. (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

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Anticonformal automorphisms and Schottky coverings.

Hidalgo, Rubén A., Costa, Anotnio F. (2001)

Annales Academiae Scientiarum Fennicae. Mathematica

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An example of degeneration on the noded Schottky space.

Rubén A. Hidalgo (1998)

Revista Matemática Complutense

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In these notes we construct explicit examples of degenerations on the noded Schottky space of genus g ≥ 3. The particularity of these degenerations is the invariance under the action of a dihedral group of order 2g. More precisely, we find a two-dimensional complex manifold in the Schottky space such that all groups (including the limit ones in the noded Schottky space) admit a fixed topological action of a dihedral group of order 2g as conformal automorphisms.

Hyperelliptic maps and surfaces

David Singerman (1997)

Mathematica Slovaca

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A Fuchsian group proof of the hyperellipticity of Riemann surfaces of genus 2.

Fuertes, Yolanda, González-Diez, Gabino (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

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A family of M-surfaces whose automorphism groups act transitively on the mirrors.

Adnan Melekoglu (2000)

Revista Matemática Complutense

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Let X be a compact Riemmann surface of genus g > 1. A symmetry T of X is an anticonformal involution. The fixed point set of T is a disjoint union of simple closed curves, each of which is called a mirror of T. If T fixes g +1 mirrors then it is called an M-symmetry and X is called an M-surface. If X admits an automorphism of order g + 1 which cyclically permutes the mirrors of T then we shall call X an M-surface with the M-property. In this paper we investigate those M-surfaces...

On the fixed-point set of an automorphism of a closed nonorientable surface

M. Izquierdo (1999)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

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On trigonal Riemann surfaces with non-unique morphims

Daniel Ying (2005)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

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On pq-hyperelliptic Riemann surfaces

Ewa Tyszkowska (2005)

Colloquium Mathematicae

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A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ϱ, called a p-hyperelliptic involution, for which X/ϱ is an orbifold of genus p. If in addition X admits a q-hypereliptic involution then we say that X is pq-hyperelliptic. We give a necessary and sufficient condition on p,q and g for existence of a pq-hyperelliptic Riemann surface of genus g. Moreover we give some conditions under which p- and q-hyperelliptic involutions of...

Non-maximal cyclic group actions on compact Riemann surfaces.

David Singerman, Paul Watson (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We say that a finite group G of automorphisms of a Riemann surface X is non-maximal in genus g if (i) G acts as a group of automorphisms of some compact Riemann surface Xg of genus g and (ii), for all such surfaces Xg , |Aut Xg| > |G|. In this paper we investigate the case where G is a cyclic group Cn of order n. If Cn acts on only finitely many surfaces of genus g, then we completely solve the problem of finding all such pairs (n,g).