dorsal/arxiv
View SchemaA generalization of Hartog's extension of line bundles
| Authors | Youssef Alaoui |
|---|---|
| Categories | |
| ArXiv ID | 2601.09645vv1 |
| URL | https://arxiv.org/abs/2601.09645 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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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"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 $\\{f\u003ec\\}$ 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 $n \\geq 3q$.",
"arxiv_id": "2601.09645",
"authors": [
"Youssef Alaoui"
],
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"math.CV"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "A generalization of Hartog\u0027s extension of line bundles",
"url": "https://arxiv.org/abs/2601.09645",
"version": "v1"
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