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arXiv · 1309.5682

Variation of the canonical height in a family of rational maps

Dragos Ghioca·Niki Myrto Mavraki
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Abstract

Let $d\ge 2$ be an integer, let $c(t)$ be any rational map, and let $f_t(z) := (z^d+t)/z$ be a family of rational maps indexed by t. For each algebraic number $t$, we let $h_{f_t}(c(t))$ be the canonical height of $c(t)$ with respect to the rational map $f_t$. We prove that the map $H(t):=h_{f_t}(c(t))$ (as $t$ varies among the algebraic numbers) is a Weil height.

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Dragos Ghioca, Niki Myrto Mavraki. 2013-09-23. Variation of the canonical height in a family of rational maps. https://arxiv.org/abs/1309.5682

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