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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 103

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 102

On gonality automorphisms of p-hyperelliptic Riemann surfaces

Content Provider	Springer Nature Link
Author	Tyszkowska, Ewa
Copyright Year	2010
Abstract	A compact Riemann surface X of genus g > 1 is saID to be a p-hyperelliptic if X admits a conformal involution ρ for which X/ρ has genus p. This notion is the particular case of so called cyclic (q, n)-gonal surface which is defined as the one admitting a conformal automorphism δ of order n such that X/δ has genus q. It is known that for g > 4 p + 1, ρ is unique And so central in the automorphism group of X. We give necessary And sufficient conditions on p And g for the existence of a Riemann surface of genus g admitting commuting p-hyperelliptic involution ρ And (q, n)-gonal automorphism δ for some prime n And we study its group of automorphisms And the number of fixed points of δ. Furthermore, we deal with automorphism groups of Riemann surfaces admitting central automorphism with at most 8 fixed points. The condition on the small number of fixed points of such an automorphism is justified by the study of p-hyperelliptic surfaces.Una superficie de Riemann compacta X de género g > 1 se dice p-hiperelíptica si X admite una involución conforme ρ, tal que X/ρ tiene género p. Las superficies p-hiperelípticas son un caso particular de las superficies (q, n)-gonales cíclicas que se definen como aquellas superficies que admiten un automorfismo conforme δ de orden q y de modo que X/δ tiene género q. En este trabajo nos restringiremos al caso en que q es un número primo mayor que 2. Es un hecho conocIDo que si g > 4 p+1, la involución ρ es única y central en el grupo de automorfismos de X. Obtenemos condiciones necesarias y suficientes sobre p y g para la existencia de superficies de Riemann de género g que admiten una involución p-hiperelíptica y un automorfismo (q, n)-gonal que conmutan. Se determina la presentación de un cociente de los grupos de automorfismos de las superficies de Riemann que admiten un automorfismo (q, n)-gonal que sea central y con 8 puntos fijos como máximo. Esta restricción sobre el número de puntos fijos se justifica por el estudio anterior de las superfices que son a la vez p-hiperelípticas y (q, n)-gonales cíclicas.
Starting Page	87
Ending Page	96
Page Count	10
File Format	PDF
ISSN	15787303
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
Volume Number	104
Issue Number	1
e-ISSN	15791505
Language	Spanish
Publisher	Springer-Verlag
Publisher Date	2010-01-01
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Automorphism groups of Riemann surfaces hyperelliptic Riemann surfaces p-hyperelliptic Riemann surfaces p-gonal Riemann surfaces Fuchsian groups Mathematics Applications of Mathematics Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Algebra and Number Theory Analysis Computational Mathematics

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