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arXiv · 2610.29082

Rigidity of Pseudoconvex Neighborhoods and Ohsawa--Takegoshi Extension

Takayuki Koike·Masakazu Takakura
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Abstract

Let $Y$ be a holomorphic section of a holomorphic submersion with one-dimensional fibers over a connected compact complex manifold. Assuming that its normal bundle is unitary flat, we prove that $Y$ admits a fundamental system of locally pseudoconvex neighborhoods if and only if it admits a holomorphic tubular neighborhood. The proof uses the sharp Ohsawa--Takegoshi extension theorem. As an application, we rule out such neighborhood systems in Ueda's example of class $(γ)$.

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Takayuki Koike, Masakazu Takakura. 2026-10-21. Rigidity of Pseudoconvex Neighborhoods and Ohsawa--Takegoshi Extension. https://arxiv.org/abs/2610.29082

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