On symmetries of pq-hyperelliptic Riemann surfaces


  • Ewa Tyszkowska University of Gdansk.




Automorphisms of Riemann surface, p-hyperelliptic Riemann surface, fixed points of automorphism, symmetry, automorfismos de superficie de Riemann, superficie de Riemann p-hiperelíptica, puntos fijos de automorfismo, simetría.


A symmetry of a Riemann surface X is an antiholomorphic involution ?. The species of ? is the integer ?k, where k is the number of connected components in the set Fix(?) of fixed points of ? and ? = -1 if X \ Fix(?) is connected and ? = 1 otherwise. A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if it admits a conformal involution ?, called a p-hyperelliptic involution, for which X/? is an orbifold of genus p. Symmetries of p-hyperelliptic Riemann surfaces has been studied by Klein for p = 0 and by Bujalance and Costa for p > 0. Here we study the species of symmetries of so called pq-hyperelliptic surface defined as a Riemann surface which is p- and q-hyperelliptic simultaneously

Author Biography

Ewa Tyszkowska, University of Gdansk.

Institute of Mathematics.


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[6] A. M. Macbeath: "Action of automorphisms of a compact Riemann surface on the first homology group". Bull. London Math. Soc. 5 (1973), 103-108.

[7] E. Tyszkowska, On pq-hyperelliptic Riemann surfaces, Coll. Math. 103 (1), (2005), 115-120.

[8] E. Tyszkowska, On p-hyperelliptic involutions of Riemann surfaces, Beiträge zur Algebra und Geometrie, to appear.



How to Cite

E. Tyszkowska, “On symmetries of pq-hyperelliptic Riemann surfaces”, Proyecciones (Antofagasta, On line), vol. 25, no. 2, pp. 179-189, May 2017.