Abstract

A real Riemann surface is a pair (R, tau), where R is a compact Riemann surface and tau : R -> R is an anticonformal involution, called a real structure of R. If R is hyperelliptic then we say that (R, tau) is a hyperelliptic real Riemann surface. In this paper we describe in terms of algebraic equations all normal (possibly branched) coverings pi: (R, tau) (5, eta) between hyperelliptic real Riemann surfaces. This extends results due to Bujalance-Cirre-Gamboa, where either the number of ovals fixed by the real structure tau is maximal, or the degree of the covering is two. In this paper we consider any real structure tau and any degree of the covering.