  Serre and Abelson have produced examples of non-homeomorphic conjugate
varieties. We show that if the field of definition of a polarized projective
variety coincides with its field of moduli then all of its conjugates have the
same topological type. This extends the class of varieties known to posses
conjugacy invariant to canonically embedded varieties. We also show that normal
complete interswections in homogeneous varieties have this property.
