A generalization of Hartog's extension of line bundles

Youssef Alaoui

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arXiv · 2601.09645

A generalization of Hartog's extension of line bundles

Youssef Alaoui

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Abstract

In this article, we prove that if $X$ is a complex manifold of dimension $n\geq 4$ such that there exists a $q$-convex with corners function $f\in F_{q}(X)$, then every holomorphic line bundle over $\{f>c\}$ extends uniquely to $X$ if $1\leq q\leq n-3$. This generalizes a well-known result obtained in \cite{ref5} for $q$-complete with corners complex manifolds with a corresponding exhaustion function $f \in F_{q}(X)$, when $n \geq 3q$.

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Youssef Alaoui. 2026-01-14. A generalization of Hartog's extension of line bundles. https://arxiv.org/abs/2601.09645

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