Riemann surfaces defined over the reals

Abstract

The known (explicit) examples of Riemann surfaces not definable over their field of moduli are not real whose field of moduli is a subfield of the reals. In this paper we provide explicit examples of real Riemann surfaces which cannot be defined over the field of moduli.

arXiv commentIn this new version, Eslam Badr has been added as a coauthor and the examples provided in the previous version has been generalised