2012/03/28 by Rubeén A. Hidalgo, Hidalgo, Rubeén A.
Mathematics · #14G99 #14H37 #14H45 #30F10 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14G99 #msc:14H37 #msc:14H45 #msc:30F10
paper · pdf · doi:10.48550/arxiv.1203.6317
Actualized version from the old one titled "The Field of Moduli of a Quadrangular Riemann surface"
arxiv created 2019/10/16 · arxiv updated 2019/10/17
Let S be a closed Riemann surface of genus g≥ 2 and let \rm Aut(S) be its group of conformal automorphisms. It is well known that if either: (i) \rm Aut(S) is trivial or (ii) S/\rm Aut(S) is an orbifold of genus zero with exactly three cone points, then S is definable over its field of moduli \mathcal M(S). In the complementary situation, explicit examples for which \mathcal M(S) is not a field of definition are known. We provide upper bounds for the minimal degree extension of \mathcal M(S) by a field of definition in terms of the quotient orbifold S/\rm Aut(S).