Several complex variables and analytic spaces Stein manifolds and coherent sheaves Concept
Stein manifold
Summary
A Stein manifold is a complex manifold with enough global holomorphic functions: they separate points and give compact holomorphically convex hulls of compact sets. Stein manifolds are the complex analogue of affine varieties, and they are exactly the closed complex submanifolds of some . On them the main problems of several complex variables, such as the Cousin problems, are governed by topology, through Cartan's theorems A and B.
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About this page
| Tag | HMCD0JBFST |
|---|---|
| URI | m2://HMCD0JBFST |
| Kind | concept |
| Writing | W0 stub |
| MSC | 32Q28, 32E10 |
| Specializes | Complex manifold, Stein space |
| Same as |
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Results about this
- Grauert's Oka principle for vector bundles
- Embedding theorem for Stein manifolds
- Behnke–Stein theorem
- Docquier–Grauert theorem
- Grauert's solution of the Levi problem for manifolds
- Oka principle
Used by
- Grauert's Oka principle for vector bundles
- Embedding theorem for Stein manifolds
- Behnke–Stein theorem
- Docquier–Grauert theorem
- Grauert's theorem on real analytic manifolds
- Grauert's solution of the Levi problem for manifolds
- Oka principle