Singularity invariants of plurisubharmonic functions and complex spaces
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915305766256640 |
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| author | Hiep, Pham Hoang |
| author_facet | Hiep, Pham Hoang |
| contents | In this paper, we combine tools from pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We establish several relationships between the singularity invariants of plurisubharmonic functions and those of holomorphic functions. These results yield a sharp lower bound for the log canonical threshold of a plurisubharmonic function. Our bound simultaneously improves upon the main result of Demailly and Pham (Acta Math. 212: 1--9, 2014), the classical result of Skoda (Bull. Soc. Math. France 100: 353--408, 1972), and the lower estimate of T. de Fernex, L. Ein and M. Mustaţǎ (Math. Res. Lett. 10: 219--236, 2003), which has played a crucial role in recent developments in birational geometry. Finally, we explore how singularity invariants associated with plurisubharmonic functions can be extended to complex spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02238 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Singularity invariants of plurisubharmonic functions and complex spaces Hiep, Pham Hoang Complex Variables 32S05 (Primary), 32S10, 32U05, 14B05, 32S25 (Secondary) In this paper, we combine tools from pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We establish several relationships between the singularity invariants of plurisubharmonic functions and those of holomorphic functions. These results yield a sharp lower bound for the log canonical threshold of a plurisubharmonic function. Our bound simultaneously improves upon the main result of Demailly and Pham (Acta Math. 212: 1--9, 2014), the classical result of Skoda (Bull. Soc. Math. France 100: 353--408, 1972), and the lower estimate of T. de Fernex, L. Ein and M. Mustaţǎ (Math. Res. Lett. 10: 219--236, 2003), which has played a crucial role in recent developments in birational geometry. Finally, we explore how singularity invariants associated with plurisubharmonic functions can be extended to complex spaces. |
| title | Singularity invariants of plurisubharmonic functions and complex spaces |
| topic | Complex Variables 32S05 (Primary), 32S10, 32U05, 14B05, 32S25 (Secondary) |
| url | https://arxiv.org/abs/2304.02238 |