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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16676 |
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| _version_ | 1866908480617578496 |
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| author | Jiao, Junpeng |
| author_facet | Jiao, Junpeng |
| contents | We study the behavior of volumes of divisors in a family. We show that the volume of a divisor on the generic fiber equals the infimum of its volumes on fibers over any dense subset of the base. As an application, we show that the volume function of a divisor is upper semicontinuous in flat families with reduced and irreducible fibers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The volume function is upper semicontinuous on families of divisors Jiao, Junpeng Algebraic Geometry We study the behavior of volumes of divisors in a family. We show that the volume of a divisor on the generic fiber equals the infimum of its volumes on fibers over any dense subset of the base. As an application, we show that the volume function of a divisor is upper semicontinuous in flat families with reduced and irreducible fibers. |
| title | The volume function is upper semicontinuous on families of divisors |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.16676 |