Displaying similar documents to “Automorphism groups of Schottky type.”

A, A, S and S of Schottky type.

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.

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.

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 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...