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On pq-hyperelliptic Klein surfaces

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Abstract

In this paper we study compact Klein surfaces of algebraic genus d > 1 admitting p- and q-hyperelliptic involutions by which we mean involutions with the orbit spaces having algebraic genera p and q. We give necessary and sufficient conditions for p, q and d to exist such surfaces. It turns out that these conditions are also sufficient for the existence of such surfaces with commuting involutions what allow us to study this class also. We study the spectrum of hyperellipticity degrees of the product of these involutions and topological type of these surfaces.

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Authors and Affiliations

  1. Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland

    Grzegorz Gromadzki & Ewa Tyszkowska

Authors
  1. Grzegorz Gromadzki
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  2. Ewa Tyszkowska
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Corresponding author

Correspondence to Grzegorz Gromadzki.

Additional information

G. Gromadzki was supported by the grant SAB 2005-0049 of the Spanish Ministry of Education and Sciences. E. Tyszkowska was supported by BW 5100-5-0198-6.

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Gromadzki, G., Tyszkowska, E. On pq-hyperelliptic Klein surfaces. manuscripta math. 122, 341–352 (2007). https://doi.org/10.1007/s00229-006-0072-0

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  • DOI: https://doi.org/10.1007/s00229-006-0072-0

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