Heights on toric varieties for singular metrics: Local theory
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911387670806528 |
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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 |