Abstract

Let S be a closed Riemann surface of genus g≥ 2 and let Aut (S) be its group of conformal automorphisms. It is well known that if either: (i) Aut (S) is trivial or (ii) S/ Aut (S) is an orbifold of genus zero with exactly three cone points, then S is definable over its field of moduli M(S). In the complementary situation, explicit examples for which M(S) is not a field of definition are known. We provide upper bounds for the minimal degree extension of M(S) by a field of definition in terms of the quotient orbifold S/ Aut (S).