Log canonical singularities of plurisubharmonic functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916412975480832 |
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| author | Kim, Dano Kollár, János |
| author_facet | Kim, Dano Kollár, János |
| contents | A plurisubharmonic weight is log canonical if it is at the critical point of turning non-integrable. Given a log canonical plurisubharmonic weight, we show that locally there always exists a log canonical `holomorphic' weight having the same non-integrable locus. The proof uses the theory of quasimonomial valuations developed by Jonsson-Mustaţǎ and Xu, as well as the minimal model program over complex analytic spaces due to Fujino and Lyu-Murayama. As a consequence, we obtain that the non-integrable locus is seminormal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16140 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Log canonical singularities of plurisubharmonic functions Kim, Dano Kollár, János Complex Variables Algebraic Geometry A plurisubharmonic weight is log canonical if it is at the critical point of turning non-integrable. Given a log canonical plurisubharmonic weight, we show that locally there always exists a log canonical `holomorphic' weight having the same non-integrable locus. The proof uses the theory of quasimonomial valuations developed by Jonsson-Mustaţǎ and Xu, as well as the minimal model program over complex analytic spaces due to Fujino and Lyu-Murayama. As a consequence, we obtain that the non-integrable locus is seminormal. |
| title | Log canonical singularities of plurisubharmonic functions |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2312.16140 |