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arXiv · 2412.15988

Continuity of heights in families and complete intersections in toric varieties

Pablo Destic·Nuno Hultberg·Michał Szachniewicz
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Abstract

We study the variation of heights of cycles in flat families over number fields or, more generally, globally valued fields. To a finite type scheme over a GVF we associate a locally compact Hausdorff space which we refer to as its GVF analytification. For a flat projective family, we prove that the height of fibres is a continuous function on the GVF analytification of the base. As an application, we prove Roberto Gualdi's conjecture on limit heights of complete intersections in toric varieties.

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Pablo Destic, Nuno Hultberg, Michał Szachniewicz. 2024-12-20. Continuity of heights in families and complete intersections in toric varieties. https://arxiv.org/abs/2412.15988

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