Additive vector fields, algebraicity and rationality (Q1914727)
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scientific article; zbMATH DE number 892572
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Additive vector fields, algebraicity and rationality |
scientific article; zbMATH DE number 892572 |
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Additive vector fields, algebraicity and rationality (English)
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9 July 1996
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We introduce a blow-up procedure for a partial resolution of the singularity of an additive vector field. This shows that a compact Kähler manifold which admits a holomorphic vector field whose zero set is projective algebraic, must be projective algebraic. By examining the blow-up centers, we prove that a projective \(n\)-dimensional manifold admitting a holomorphic vector field with nonempty isolated zeroes is rational for dimension \(n \leq 5\).
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algebraicity of compact Kähler manifold
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rationality of projection manifold
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resolution of the singularity
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blow-up
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