Opuscula Math. 29, no. 4 (2009), 443-452
http://dx.doi.org/10.7494/OpMath.2009.29.4.443

Opuscula Mathematica

# Topological classification of conformal actions on p-hyperelliptic and (q,n)-gonal Riemann surfaces

Ewa Tyszkowska

Abstract. A compact Riemann surface $$X$$ of genus $$g \gt 1$$ is said to be $$p$$-hyperelliptic if $$X$$ admits a conformal involution $$\rho$$ for which $$X / \rho$$ has genus $$p$$. A conformal automorphism $$\delta$$ of prime order $$n$$ such that $$X / \delta$$ has genus $$q$$ is called a $$(q,n)$$-gonal automorphism. Here we study conformal actions on $$p$$-hyperelliptic Riemann surface with $$(q,n)$$-gonal automorphism.

Keywords: $$p$$-hyperelliptic Riemann surface, automorphism of a Riemann surface.

Mathematics Subject Classification: 30F20, 30F50, 14H37, 20H30, 20H10.

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• Ewa Tyszkowska
• University of Gdańsk, Institute of Mathematics, ul. Wita Stwosza 57, 80-952 Gdansk, Poland
• Revised: 2009-07-21.
• Accepted: 2009-07-27.