On certain existence questions for pseudoconvex hypersurfaces in complex manifolds (Q697324)
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scientific article; zbMATH DE number 1801556
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On certain existence questions for pseudoconvex hypersurfaces in complex manifolds |
scientific article; zbMATH DE number 1801556 |
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On certain existence questions for pseudoconvex hypersurfaces in complex manifolds (English)
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17 September 2002
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The paper presents some very interesting existence and nonexistence results for certain smoothly bounded pseudoconvex domains in complex manifolds. For example, it is shown that a pseudoconvex domain with \(C^{1}\)-smooth boundary in the complex projective space of dimension greater or equal than 2 does not contain any compact complex subvarieties of positive dimension. An open problem on the subject (under the form of a conjecture) is also presented.
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pseudoconvex domain
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complex subvarieties
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(nonconstant) holomorphic function
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existence
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nonexistence
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