Endomorphisms of Bounded Height and Resultant

Abstract

Let K be an algebraic number field. For a degree d rational morphism of projective n-space defined over K let R denote its minimal resultant ideal. For a fixed height function on the moduli space of dynamical systems this paper shows that all such morphisms of bounded height and resultant are contained in finitely many PGL(K) equivalence classes. This answers a question of Silverman in the affirmative.