Topological classification of conformal actions on p-hyperelliptic and (q,n)-gonal Riemann surfaces
Abstract. A compact Riemann surface \(X\) of genus \(g \gt 1\) is said to be \(p\)-hyperelliptic if \(X\) admits a conformal involution \(\rho\) for which \(X / \rho\) has genus \(p\). A conformal automorphism \(\delta\) of prime order \(n\) such that \(X / \delta\) has genus \(q\) is called a \((q,n)\)-gonal automorphism. Here we study conformal actions on \(p\)-hyperelliptic Riemann surface with \((q,n)\)-gonal automorphism.
Keywords: \(p\)-hyperelliptic Riemann surface, automorphism of a Riemann surface.
Mathematics Subject Classification: 30F20, 30F50, 14H37, 20H30, 20H10.