Intermediate Pseudoconvexity of Fiber Bundles

Masanori Adachi; Seungjae Lee; Aeryeong Seo

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arXiv · 2606.15533

Intermediate Pseudoconvexity of Fiber Bundles

Masanori Adachi·Seungjae Lee·Aeryeong Seo

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Abstract

In this paper, we investigate the pseudoconvexity of locally trivial holomorphic ball bundles over compact Riemann surfaces of genus $\geq 2$, as well as the intermediate pseudoconvexity of their complements in the associated projective space bundles. Inspired by Brunella's work, we prove that any such ball bundle is $1$-convex, while its complement is $n$-convex, where $n$ denotes the dimension of the ball fiber, provided that the bundle admits a harmonic section with a regular point.

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Masanori Adachi, Seungjae Lee, Aeryeong Seo. 2026-06-14. Intermediate Pseudoconvexity of Fiber Bundles. https://arxiv.org/abs/2606.15533

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