On Lelong numbers of plurisubharmonic functions on complex spaces
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| Format: | Preprint |
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2025
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| _version_ | 1866915213092061184 |
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| author | Hai, Le Mau Hiep, Pham Hoang Tung, Trinh |
| author_facet | Hai, Le Mau Hiep, Pham Hoang Tung, Trinh |
| contents | In this paper, we introduce the notion of strong locally irreducible complex spaces $\widetilde{X}$. Based on this notion we prove the equality $\barν_φ(x)=$ mult$(\widetilde{X},x). ν_φ(x)$ for all $x\in \widetilde{X}$, where $\barν_φ(x)$ is the projective mass of a plurisubharmonic function $φ$ at $x$ and mult$(\widetilde{X},x)$ is the multiplicity of $\widetilde{X}$ at $x$ and $ν_φ(x)$ is Lelong number of $φ$ at $x$. Moreover, we show that the closure of the upper-level sets $\{z\in \widetilde{X}:ν_φ(z)\geq c\}$ of a plurisubharmonic function $φ$ on a strong locally irreducible complex space $\widetilde{X}$ is a subvariety of $\widetilde{X}$ for all $c\geq 0$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_19497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Lelong numbers of plurisubharmonic functions on complex spaces Hai, Le Mau Hiep, Pham Hoang Tung, Trinh Complex Variables 32C15, 32C25, 32C30, 32U25, 32U40, 32W20 In this paper, we introduce the notion of strong locally irreducible complex spaces $\widetilde{X}$. Based on this notion we prove the equality $\barν_φ(x)=$ mult$(\widetilde{X},x). ν_φ(x)$ for all $x\in \widetilde{X}$, where $\barν_φ(x)$ is the projective mass of a plurisubharmonic function $φ$ at $x$ and mult$(\widetilde{X},x)$ is the multiplicity of $\widetilde{X}$ at $x$ and $ν_φ(x)$ is Lelong number of $φ$ at $x$. Moreover, we show that the closure of the upper-level sets $\{z\in \widetilde{X}:ν_φ(z)\geq c\}$ of a plurisubharmonic function $φ$ on a strong locally irreducible complex space $\widetilde{X}$ is a subvariety of $\widetilde{X}$ for all $c\geq 0$. |
| title | On Lelong numbers of plurisubharmonic functions on complex spaces |
| topic | Complex Variables 32C15, 32C25, 32C30, 32U25, 32U40, 32W20 |
| url | https://arxiv.org/abs/2503.19497 |