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arXiv · 2212.00114

Holomorphic extension in holomorphic fiber bundles with (1,0)-compactifiable fiber

Sergey Feklistov
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Abstract

We use the Leray spectral sequence for the sheaf cohomology groups with compact supports to obtain a vanishing result. The stalks of sheaves $R^{\bullet}\phi_{!}\mathcal{O}$ for the structure sheaf $\mathcal{O}$ on the total space of a holomorphic fiber bundle $\phi$ 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 K\"unnet formulas, properties of an inductive topology (with respect to the pair of spaces) on the stalks of the sheaf $R^{1}\phi_{!}\mathcal{O}$ 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.

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Sergey Feklistov. 2022-11-30. Holomorphic extension in holomorphic fiber bundles with (1,0)-compactifiable fiber. https://arxiv.org/abs/2212.00114

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