Holomorphic vector bundles on open subsets of Stein manifolds (Q1870911)
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scientific article; zbMATH DE number 1910265
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Holomorphic vector bundles on open subsets of Stein manifolds |
scientific article; zbMATH DE number 1910265 |
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Holomorphic vector bundles on open subsets of Stein manifolds (English)
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6 January 2004
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Every vector bundle \(E\) on a Stein manifold has holomorphic sections, in particular, there is a line bundle \(A\) with a nonzero map \( A \rightarrow E.\) Let \(M\) be a connected 2-dimensional Stein manifold with \(H^2(M,{\mathbb Z}),\) and let \(X= M-S\) where \(S\) is discrete and nonempty. The author shows that there exists a vector bundle \(E\) on \(X\) such that there is no line bundle \(A\) with a nonzero map \(A\rightarrow X.\)
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holomorphic bundle
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Stein space
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