Zhou valuations and jumping numbers
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915057339727872 |
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| author | Bao, Shijie Guan, Qi'an Yuan, Zheng |
| author_facet | Bao, Shijie Guan, Qi'an Yuan, Zheng |
| contents | In this article, we prove that for any Zhou valuation $ν$, there exists a graded sequence of ideals $\mathfrak{a}_{\bullet}$ and a nonzero ideal $\mathfrak{q}$ such that $ν$ $\mathscr{A}-$computes the jumping number $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$, and that for the subadditive sequence $\mathfrak{b}^φ_{\bullet}$ related to a plurisubharmonic function $φ$, there exists a Zhou valuation which $\mathscr{A}-$computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{b}^φ_{\bullet})$, where the ``$\mathscr{A}-$compute'' coincides with the ``compute'' in Jonsson-Mustaţă's Conjecture when the Zhou valuation $ν$ is quasimonomial. There are also some results obtained for Zhou valuations, including a characterization for a valuation being a Zhou valuation, and a denseness property of the cone of Zhou valuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06565 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Zhou valuations and jumping numbers Bao, Shijie Guan, Qi'an Yuan, Zheng Complex Variables Algebraic Geometry In this article, we prove that for any Zhou valuation $ν$, there exists a graded sequence of ideals $\mathfrak{a}_{\bullet}$ and a nonzero ideal $\mathfrak{q}$ such that $ν$ $\mathscr{A}-$computes the jumping number $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$, and that for the subadditive sequence $\mathfrak{b}^φ_{\bullet}$ related to a plurisubharmonic function $φ$, there exists a Zhou valuation which $\mathscr{A}-$computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{b}^φ_{\bullet})$, where the ``$\mathscr{A}-$compute'' coincides with the ``compute'' in Jonsson-Mustaţă's Conjecture when the Zhou valuation $ν$ is quasimonomial. There are also some results obtained for Zhou valuations, including a characterization for a valuation being a Zhou valuation, and a denseness property of the cone of Zhou valuations. |
| title | Zhou valuations and jumping numbers |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2311.06565 |