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Proyecciones (Antofagasta)

Print version ISSN 0716-0917


TYSZKOWSKA, EWA. ON SYMMETRIES OF PQ-HYPERELLIPTIC RIEMANN SURFACES. Proyecciones (Antofagasta) [online]. 2006, vol.25, n.2, pp.179-189. ISSN 0716-0917.

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.

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