Maximal ratio of coefficients of divisors and an upper bound for height for rational maps

Abstract

When we have a morphism f : P^n -> P^n, then we have an inequality \frac{1}{°f} h(f(P)) +C > h(P) which provides a good upper bound of $h(P)$. However, if $f$ is a rational map, then \frac{1}{°f} h(f(P))+C cannot be an upper bound of h(P). In this paper, we will define the $D$-ratio of a rational map $f$ which will replace the degree of a morphism in the height inequality of h(P).

References in corpus (2)

• Height Estimates for Equidimensional Dominant Rational Maps
• An upper bound for the height for regular affine automorphisms of A^n

Cited by in corpus (3)

• Integral Points and Relative Sizes of Coordinates of Orbits in P^N
• The equidistribution of small point for strongly regular pairs of polynomial maps
• Finiteness of commutable maps of bounded degree