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arXiv · 2208.01597

Height coincidences in products of the projective line

Niki Myrto Mavraki·Harry Schmidt·Robert Wilms
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Abstract

We consider hypersurfaces in $(\mathbb{P}^1)^n$ that contain a generic sequence of small dynamical height with respect to a split map and project onto $n-1$ coordinates. We show that these hypersurfaces satisfy strong coincidence relations between their points with zero height coordinates. More precisely, it holds that in a Zariski-open dense subset of such a hypersurface $n-1$ coordinates have height zero if and only if all coordinates have height zero. This is a key step in the resolution of the dynamical Bogomolov conjecture for split maps.

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Niki Myrto Mavraki, Harry Schmidt, Robert Wilms. 2022-08-02. Height coincidences in products of the projective line. https://arxiv.org/abs/2208.01597

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