Metrized ample line bundles in non-Archimedean geometry II
Yanbo Fang

TL;DR
This paper introduces Shilov finite metrics on ample line bundles in non-Archimedean geometry, providing new tools for calculating metric distortions and proving an arithmetic Hilbert-Samuel formula, along with defining equidistribution measures.
Contribution
It defines Shilov finite metrics, computes determinant metric distortions, and proves an arithmetic Hilbert-Samuel formula using non-Archimedean techniques.
Findings
Introduction of Shilov finite metrics
Calculation of determinant metric distortion
Analytic proof of arithmetic Hilbert-Samuel formula
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.
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Taxonomy
TopicsGeometry and complex manifolds · advanced mathematical theories · Holomorphic and Operator Theory
