Metrized ample line bundles in non-Archimedean geometry II

2025/11/26 by Fang, Yanbo
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #advanced mathematical theories

paper · doi:10.48550/arxiv.2511.21835

openalex publication_date 2025/11/26 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

We introduce a class of semipositive metrics on ample line bundles in non-Archimedean geometry, called Shilov finite metrics. We calculate the determinant metric distorsion in the exact sequence induced by a global section using non-Archimedean norm reduction techniques. This leads to an analytic proof to the arithmetic Hilbert-Samuel formula over a local place for a semipositively metrized ample line bundle. We define the equidistribution measure associated to a Shilov finite metric and solve the corresponding inverse problem.

Citations

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• Solution to a non-Archimedean Monge-Ampère equation
• Les espaces de Berkovich sont angéliques
• Countability properties of some Berkovich spaces
• Free basis consisting of strictly small sections

Related

• Singular semipositive metrics in non-Archimedean geometry
• On Zhang's semipositive metrics
• Spaces of norms, determinant of cohomology and Fekete points in\n non-Archimedean geometry
• Non-Archimedean metric extension for semipositive line bundles
• Partial Okounkov bodies and Duistermaat--Heckman measures of non-Archimedean metrics