Algebraic Zhou valuations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918163053019136 |
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| author | Bao, Shijie Guan, Qi'an Zhou, Lin |
| author_facet | Bao, Shijie Guan, Qi'an Zhou, Lin |
| contents | In this paper, we generalize Zhou valuations, originally defined on complex domains, to the framework of general schemes. We demonstrate that an algebraic version of the Jonsson--Mustaţă conjecture is equivalent to the statement that every Zhou valuation is quasi-monomial. By introducing a mixed version of jumping numbers and Tian functions associated with valuations, we obtain characterizations of a valuation being a Zhou valuation or computing some jumping number using the Tian functions. Furthermore, we establish the correspondence between Zhou valuations in algebraic settings and their counterparts in analytic settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic Zhou valuations Bao, Shijie Guan, Qi'an Zhou, Lin Algebraic Geometry Complex Variables 14F18, 12J20, 14B05, 32U05, 32U35 In this paper, we generalize Zhou valuations, originally defined on complex domains, to the framework of general schemes. We demonstrate that an algebraic version of the Jonsson--Mustaţă conjecture is equivalent to the statement that every Zhou valuation is quasi-monomial. By introducing a mixed version of jumping numbers and Tian functions associated with valuations, we obtain characterizations of a valuation being a Zhou valuation or computing some jumping number using the Tian functions. Furthermore, we establish the correspondence between Zhou valuations in algebraic settings and their counterparts in analytic settings. |
| title | Algebraic Zhou valuations |
| topic | Algebraic Geometry Complex Variables 14F18, 12J20, 14B05, 32U05, 32U35 |
| url | https://arxiv.org/abs/2505.19451 |