%0 Journal Article
%T A simple remark on fields of definition
%A Rub¨¦n Hidalgo
%J Proyecciones (Antofagasta)
%D 2012
%I Universidad Cat¨®lica del Norte
%X Let K< L be an extension of fields, in characteristic zero, with L algebraically closed and let ¡¥K < L be the algebraic closure of K in L. Let X and Y be irreducible projective algebraic varieties, X defined over ¡¥K and Y defined over L, and let ¦Ð : X ¡úY be a non-constant morphism, defined over L. If we assume that ¡¥K ¡Ù L, then one may wonder if Y is definable over ¡¥K. In the case that K = Q, L = C and that X and Y are smooth curves, a positive answer was obtained by Gonzalez-Diez. In this short note we provide simple conditions to have a positive answer to the above question. We also state a conjecture for a class of varieties of general type.
%K Algebraic curves
%K field of moduli
%K field of definition
%U http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100003