Abstract

The known examples of explicit equations for Riemann surfaces whose field of moduli is different from their field of definition, are all hyperelliptic. In this paper we construct a family of equations for non-hyperelliptic Riemann surfaces, each of them is isomorphic to its conjugate Riemann surface, but none of them admit an anticonformal automorphism of order 2; that is, each of them has its field of moduli, but not a field of definition, contained in R. These appear to be the first explicit such examples in the non-hyperelliptic case. © 2009 Birkhä user Verlag Basel Switzerland.