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arXiv · 1408.5416

Variation of the canonical height for polynomials in several variables

Patrick Ingram
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Abstract

Let K be a number field, X/K a curve, and f/X a family of endomorphisms of projective N-space. It follows from a result of Call and Silverman that the canonical height associated to the family f, evaluated along a section, differs from a Weil height on the base by little-o of a Weil height. In the case where f is a family with an invariant hyperplane, whose restriction to this invariant hyperplane is isotrivial, we improve this by showing that the canonical height along a section differs from a Weil height on the base by a bounded amount.

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Patrick Ingram. 2014-08-22. Variation of the canonical height for polynomials in several variables. https://arxiv.org/abs/1408.5416

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