A generalization of Hartog's extension of line bundles

Abstract

In this article, we prove that if $X$ is a complex manifold of dimension $n\ge 4$ 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 $1\le q\le n-3$. 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 $n\ge 3q$.

7 pages, Submitted to Complex Variables and Elliptic Equations