Holomorphic extension in holomorphic fiber bundles with (1,0)-compactifiable fiber
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913730490531840 |
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| author | Feklistov, Sergey |
| author_facet | Feklistov, Sergey |
| contents | We use the Leray spectral sequence for the sheaf cohomology groups with compact supports to obtain a vanishing result. The stalks of sheaves $R^{\bullet}ϕ_{!}\mathcal{O}$ for the structure sheaf $\mathcal{O}$ on the total space of a holomorphic fiber bundle $ϕ$ has canonical topology structures. Using the standard \vCech argument we prove a density lemma for QDFS-topology on this stalks. In particular, we obtain a vanishing result for holomorphic fiber bundles with Stein fibers. Using Künnet formulas, properties of an inductive topology (with respect to the pair of spaces) on the stalks of the sheaf $R^{1}ϕ_{!}\mathcal{O}$ and a cohomological criterion for the Hartogs phenomenon we obtain the main result on the Hartogs phenomenon for the total space of holomorphic fiber bundles with (1,0)-compactifiable fibers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00114 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Holomorphic extension in holomorphic fiber bundles with (1,0)-compactifiable fiber Feklistov, Sergey Complex Variables 32A10, 32A70, 32D20, 32L05, 32C35, 55N30 We use the Leray spectral sequence for the sheaf cohomology groups with compact supports to obtain a vanishing result. The stalks of sheaves $R^{\bullet}ϕ_{!}\mathcal{O}$ for the structure sheaf $\mathcal{O}$ on the total space of a holomorphic fiber bundle $ϕ$ has canonical topology structures. Using the standard \vCech argument we prove a density lemma for QDFS-topology on this stalks. In particular, we obtain a vanishing result for holomorphic fiber bundles with Stein fibers. Using Künnet formulas, properties of an inductive topology (with respect to the pair of spaces) on the stalks of the sheaf $R^{1}ϕ_{!}\mathcal{O}$ and a cohomological criterion for the Hartogs phenomenon we obtain the main result on the Hartogs phenomenon for the total space of holomorphic fiber bundles with (1,0)-compactifiable fibers. |
| title | Holomorphic extension in holomorphic fiber bundles with (1,0)-compactifiable fiber |
| topic | Complex Variables 32A10, 32A70, 32D20, 32L05, 32C35, 55N30 |
| url | https://arxiv.org/abs/2212.00114 |