Abstract
A symmetry of a Riemann surface X is an antiholomorphic involution φ .T he species ofφ is the integer ek ,w herek is the number of connected components in the set Fix(φ) of fixed points of φ and e = −1 if X Fix(φ) 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 ρ ,c alled ap-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 -a nd q-hyperelliptic simultaneously.
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