HEIGHT INEQUALITY FOR RATIONAL MAPS AND BOUNDS FOR PREPERIODIC POINTS

In this paper, we introduce the D-ratio of a rational map f : P-n -> P-n, defined over (Q) over bar whose indeterminacy locus is contained in a hyperplane H on P-n. The D-ratio r(f; <(V))over bar> characterizes endomorphisms and provides a useful height inequality on P-n (<(Q))over bar> \ H. We also provide a dynamical application: preperiodic points of dynamical systems of small D-ratio are of bounded height.