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arXiv · 1002.3357

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

ChongGyu Lee
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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).

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ChongGyu Lee. 2011-10-07. Maximal ratio of coefficients of divisors and an upper bound for height for rational maps. https://arxiv.org/abs/1002.3357

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