Metrized ample line bundles in non-Archimedean geometry II
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911289665650688 |
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| author | Fang, Yanbo |
| author_facet | Fang, Yanbo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metrized ample line bundles in non-Archimedean geometry II Fang, Yanbo Algebraic Geometry 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. |
| title | Metrized ample line bundles in non-Archimedean geometry II |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2511.21835 |