Displaying similar documents to “On the pole placement problem for linear systems of arbitrary genus.”

On the theorem of de Franchis

Alan Howard, Andrew J. Sommese (1983)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze


On pq-hyperelliptic Riemann surfaces

Ewa Tyszkowska (2005)

Colloquium Mathematicae


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...

On commutativity and ovals for a pair of symmetries of a Riemann surface

Ewa Kozłowska-Walania (2007)

Colloquium Mathematicae


We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry...

Non-maximal cyclic group actions on compact Riemann surfaces.

David Singerman, Paul Watson (1997)

Revista Matemática de la Universidad Complutense de Madrid


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).