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Rigidity of Pseudoconvex Neighborhoods and Ohsawa--Takegoshi Extension
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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BibTeX
@misc{koike2026rigidity,
title = {{Rigidity of Pseudoconvex Neighborhoods and Ohsawa--Takegoshi Extension}},
author = {Takayuki Koike and Masakazu Takakura},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29082},
eprint = {2610.29082},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29082},
}
RIS
TY - UNPB
TI - Rigidity of Pseudoconvex Neighborhoods and Ohsawa--Takegoshi Extension
AU - Takayuki Koike
AU - Masakazu Takakura
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29082
UR - https://arxiv.org/abs/2610.29082
AB - 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).
ER -