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Stein Criteria for Holomorphic Fibre Bundles
Abstract
In this paper, we study Steinness of holomorphic fibre bundles. Over a compact Riemann surface, we prove that every holomorphic ball bundle is weakly $1$-complete and that its total space is Stein if and only if it admits no holomorphic section. We also obtain higher-dimensional Stein criteria for reductive ball bundles and affine bundles in terms of positivity of the canonical class. A topological obstruction to the $1$-convexity of holomorphic fibre bundles is also established.
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BibTeX
@misc{takakura2026stein,
title = {{Stein Criteria for Holomorphic Fibre Bundles}},
author = {Masakazu Takakura},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01693},
eprint = {2611.01693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01693},
}
RIS
TY - UNPB
TI - Stein Criteria for Holomorphic Fibre Bundles
AU - Masakazu Takakura
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01693
UR - https://arxiv.org/abs/2611.01693
AB - In this paper, we study Steinness of holomorphic fibre bundles. Over a compact Riemann surface, we prove that every holomorphic ball bundle is weakly $1$-complete and that its total space is Stein if and only if it admits no holomorphic section. We also obtain higher-dimensional Stein criteria for reductive ball bundles and affine bundles in terms of positivity of the canonical class. A topological obstruction to the $1$-convexity of holomorphic fibre bundles is also established.
ER -