Heights on toric varieties for singular metrics: Local theory

Fuente: arXiv
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Main Author: Alvarez, Gari Y. Peralta
Format: Preprint
Published: 2026
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author Alvarez, Gari Y. Peralta
author_facet Alvarez, Gari Y. Peralta
contents 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 Kühn in 2016.
format Preprint
id arxiv_https___arxiv_org_abs_2601_14167
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Heights on toric varieties for singular metrics: Local theory
Alvarez, Gari Y. Peralta
Algebraic Geometry
Number Theory
Primary 14G40, Secondary 14M25, 32U05, 14T90, 44A15
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 Kühn in 2016.
title Heights on toric varieties for singular metrics: Local theory
topic Algebraic Geometry
Number Theory
Primary 14G40, Secondary 14M25, 32U05, 14T90, 44A15
url https://arxiv.org/abs/2601.14167