  Let Hom^N_d be the set of morphisms of degree d from P^N to itself. For f an
element of PGL_{N+1}, let phi^f represent the conjugation action f^{-1} phi f.
Let M^N_d = Hom_d^N/PGL_{N+1} be the moduli space of degree d morphisms of P^N.
A field of definition for class of morphisms is a field over which at least one
morphism in the class is defined. The field of moduli for a class of morphisms
is the fixed field of the set of Galois elements fixing that class. Every field
of definition contains the field of moduli. In this article, we give a
sufficient condition for the field of moduli to be a field of definition for
morphisms whose stabilizer group is trivial.
