首页|On gonality automorphisms of p-hyperelliptic Riemann surfaces
On gonality automorphisms of p-hyperelliptic Riemann surfaces
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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 > Ap + 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.
automorphism groups of riemann surfaceshyperelliptic riemann surfacesp-hyperelliptic riemann surfacesp-gonal riemann surfacesfuchsian groups
Ewa Tyszkowska
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Institute of Mathematics, Gdansk University, Wita Stwosza 57, 80-952 Gdansk, Poland
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