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arXiv · 2601.14167

Heights on toric varieties for singular metrics: Local theory

Gari Y. Peralta Alvarez
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Abstract

We show that the (toric) local height of a toric variety with respect to a semipositive torus-invariant singular metric is given by the integral of a concave function over a compact convex set. This generalizes a result of Burgos, Philippon, and Sombra for the case of continuous metrics and answers a question raised by Burgos, Kramer, and K\"uhn in 2016.

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Gari Y. Peralta Alvarez. 2026-01-20. Heights on toric varieties for singular metrics: Local theory. https://arxiv.org/abs/2601.14167

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