## Proyecciones (Antofagasta)

*Print version* ISSN 0716-0917

#### Abstract

TYSZKOWSKA, EWA. **ON SYMMETRIES OF PQ-HYPERELLIPTIC RIEMANN SURFACES**.* Proyecciones (Antofagasta)* [online]. 2006, vol.25, n.2, pp.179-189.
ISSN 0716-0917. http://dx.doi.org/10.4067/S0716-09172006000200004.

*A symmetry of a Riemann surface X is an antiholomorphic involution f. The species of f is the integer ek, where k is the number of connected components in the set Fix(f) of fixed points of f and e = -1 if X \ Fix(f) is connected and e = 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*

**Keywords
:
***p-hyperelliptic Riemann surface*; *automorphisms of Riemann surface*; *fixed points of automorphism*; *symmetry*.