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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2508.01753 |
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| _version_ | 1866909719359127552 |
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| author | Varolin, Dror |
| author_facet | Varolin, Dror |
| contents | We examine the relationship between positivity of a vector bundle E and the problem of $L^2$ extension of holomorphic E-valued forms of top degree. In particular, we show by example that Griffiths positivity is not enough. Though the sufficiency of Nakano positivity of E has been known for some time, we provide another proof along the lines of Berndtsson and Lempert. For such a proof we establish a vector bundle analogue of a well-known result of Berndtsson. This result is of independent interest and should have many other useful applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01753 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positivity and $\mathbf{L^2}$ Extension Varolin, Dror Complex Variables We examine the relationship between positivity of a vector bundle E and the problem of $L^2$ extension of holomorphic E-valued forms of top degree. In particular, we show by example that Griffiths positivity is not enough. Though the sufficiency of Nakano positivity of E has been known for some time, we provide another proof along the lines of Berndtsson and Lempert. For such a proof we establish a vector bundle analogue of a well-known result of Berndtsson. This result is of independent interest and should have many other useful applications. |
| title | Positivity and $\mathbf{L^2}$ Extension |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2508.01753 |