A cohomological characterization of \({\mathbb{P}}^ n\) (Q796596)
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scientific article; zbMATH DE number 3865468
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A cohomological characterization of \({\mathbb{P}}^ n\) |
scientific article; zbMATH DE number 3865468 |
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A cohomological characterization of \({\mathbb{P}}^ n\) (English)
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1983
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The author characterizes \(({\mathbb{P}}^ n,{\mathcal O}(1))\) among all (X,L) by \(H^ 0(\theta_ X\otimes L^{-1})=0\) for the tangent bundle \(\theta_ X\), provided X is non-singular projective, \(\dim X>1,\) and L is an ample line bundle. Actually he proves a stronger result where X is only required to be projective and normal.
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characterization of projective space
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ample line bundle
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