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Variation of the canonical height in a family of rational maps

University of British Columbia

Let d ≥2 be an integer, let c ∈ ℚ(t) be a rational map, and let f_t(z) = (z^d+t)/z be a family of rational maps indexed by t. For each t = λ algebraic number, we let ĥ_(f_λ)(c(λ)) be the canonical height of c(λ) with respect to the rational map f_λ; also we let ĥ_f(c) be the canonical height of c on the generic fiber of the above family of rational maps. We prove that there exists a constant C depending only on c such that for each algebraic number λ, |ĥ_(f_λ)(c(λ))-ĥ_f(c)h(λ)| ≤C. [Formula missing] This improves a result of Call and Silverman for this family of rational maps.

Text

2014-04-17

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/46480

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/