Ross-Witt Nyström correspondence and Ohsawa-Takegoshi extension
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916859515764736 |
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| author | He, Yan Testorf, Johannes Wang, Xu |
| author_facet | He, Yan Testorf, Johannes Wang, Xu |
| contents | We obtain a general Ohsawa-Takegoshi extension theorem by using the Ross-Witt Nyström correspondence picture and Berndtsson's theorem in \cite{Bern20}. In the test configuration ($\mathbb C^*$-degeneration) case, our approach gives a quick proof of the Ohsawa-Takegoshi extension theorem without taking limit or using singular weight, which is very different from the Ohsawa-Chen-Blocki-Guan-Zhou approach and the Berndtsson-Lempert approach. Another advantage of our approach is that it fits better to the sharp estimate for the weighted Bergman kernel on compact manifold. Applications include a sharp lower bound of the Bergman kernel for compact Riemann surfaces and a non-vanishing theorem in terms of (weighted) Okounkov bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03840 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ross-Witt Nyström correspondence and Ohsawa-Takegoshi extension He, Yan Testorf, Johannes Wang, Xu Complex Variables Algebraic Geometry Differential Geometry We obtain a general Ohsawa-Takegoshi extension theorem by using the Ross-Witt Nyström correspondence picture and Berndtsson's theorem in \cite{Bern20}. In the test configuration ($\mathbb C^*$-degeneration) case, our approach gives a quick proof of the Ohsawa-Takegoshi extension theorem without taking limit or using singular weight, which is very different from the Ohsawa-Chen-Blocki-Guan-Zhou approach and the Berndtsson-Lempert approach. Another advantage of our approach is that it fits better to the sharp estimate for the weighted Bergman kernel on compact manifold. Applications include a sharp lower bound of the Bergman kernel for compact Riemann surfaces and a non-vanishing theorem in terms of (weighted) Okounkov bodies. |
| title | Ross-Witt Nyström correspondence and Ohsawa-Takegoshi extension |
| topic | Complex Variables Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2311.03840 |