A generalization of Hartog's extension of line bundles
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 $n \geq 3q$.
Fields of Study & Subjects
Geometry and complex manifolds
Holomorphic and Operator Theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 14 January 2026
- Document type
- Preprint