The log-plurisubharmonicity of fiberwise $ξ-$Bergman kernels for variant functionals
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| Format: | Preprint |
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2023
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| _version_ | 1866913569857077248 |
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| author | Bao, Shijie Guan, Qi'an Yuan, Zheng |
| author_facet | Bao, Shijie Guan, Qi'an Yuan, Zheng |
| contents | In this paper, we establish the log-plurisubharmonicity of fiberwise $ξ$-Bergman kernels for a family of variant functionals, thereby addressing a question posed by Bo Berndtsson to the authors. As an application, we prove that for a plurisubharmonic function $ϕ$ and a locally finitely generated ideal sheaf $\mathscr{I}$ on the polydisc $Δ^{n+m}=Δ^n\timesΔ^m$, the set of points $w\inΔ^m$ for which $\mathcal{I}(ϕ|_{H_w})_{(o,w)}\subseteq (\mathscr{I}|_{H_w})_{(o,w)}$ is a pluripolar set, where $H_w$ represents the fiber over $w$, and $\mathcal{I}(ϕ|_{H_w})$ denotes the multiplier ideal sheaf of $ϕ|_{H_w}$ on $H_w$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_16525 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The log-plurisubharmonicity of fiberwise $ξ-$Bergman kernels for variant functionals Bao, Shijie Guan, Qi'an Yuan, Zheng Complex Variables 32A36, 32A70, 32D15, 32L05, 32U05 In this paper, we establish the log-plurisubharmonicity of fiberwise $ξ$-Bergman kernels for a family of variant functionals, thereby addressing a question posed by Bo Berndtsson to the authors. As an application, we prove that for a plurisubharmonic function $ϕ$ and a locally finitely generated ideal sheaf $\mathscr{I}$ on the polydisc $Δ^{n+m}=Δ^n\timesΔ^m$, the set of points $w\inΔ^m$ for which $\mathcal{I}(ϕ|_{H_w})_{(o,w)}\subseteq (\mathscr{I}|_{H_w})_{(o,w)}$ is a pluripolar set, where $H_w$ represents the fiber over $w$, and $\mathcal{I}(ϕ|_{H_w})$ denotes the multiplier ideal sheaf of $ϕ|_{H_w}$ on $H_w$. |
| title | The log-plurisubharmonicity of fiberwise $ξ-$Bergman kernels for variant functionals |
| topic | Complex Variables 32A36, 32A70, 32D15, 32L05, 32U05 |
| url | https://arxiv.org/abs/2303.16525 |