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

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

2010-02-17

arxiv.org/abs/1002.3357v2

Mathematics

Number Theory

Scientific paper

When we have a morphism f : P^n -> P^n, then we have an inequality \frac{1}{\deg 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}{\deg 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).

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