Resumen de On symmetries of pq-hyperelliptic Riemann surfaces

Ewa Tyszkowska

• A symmetry of a Riemann surface X is an antiholomorphic involution φ. The species of φ is the integer εk, where k is the number of connected components in the set Fix(φ) of fixed points of φ and ε = -1 if X \ Fix(φ) is connected and ε = 1 otherwise. A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if it admits a conformal involution ρ, called a p-hyperelliptic involution, for which X/ρ 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