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arXiv · 2611.01693

Stein Criteria for Holomorphic Fibre Bundles

Masakazu Takakura
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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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Masakazu Takakura. 2026-11-01. Stein Criteria for Holomorphic Fibre Bundles. https://arxiv.org/abs/2611.01693

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