Symmetries of real cyclic \(p\)-gonal Riemann surfaces
A symmetry of a compact Riemann surface \(X\) is an antiholomorphic involution \(\sigma:X\to X\). The paper under review deals with triples \((X,f,\sigma)\), where \(\sigma\) is a symmetry of the compact Riemann surface \(X\) and \(f:X\to\Sigma\) is a cyclic \(p\)-gonal morphism onto the Riemann sphere \(\Sigma\) such that \(f\circ\sigma= c\circ f\) where \(p\) is an odd prime and \(c:\Sigma\to\Sigma\) is complex conjugation. The main result of the paper which is carefully and very detailed proved by using the combinatorial theory of Riemann surfaces, is theorem 3, where the specia (i.e., the number of connected components of the fixed point set of \(\sigma\) and the orientability character of the quotient \(X/\langle \sigma\rangle)\) of all occuring symmetries \(\sigma\) of \(X\) are calculated.
scientific article; zbMATH DE number 2113413