Heights on toric varieties for singular metrics: Local theory
Algebraic Geometry
2026-01-21 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.2601.14167,
title = {Heights on toric varieties for singular metrics: Local theory},
author = {Gari Y. Peralta Alvarez},
journal= {arXiv preprint arXiv:2601.14167},
year = {2026}
}