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A cohomological characterization of \({\mathbb{P}}^ n\). (English) Zbl 0544.14013

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.
Reviewer: K.Lamotke

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
32C35 Analytic sheaves and cohomology groups
32L05 Holomorphic bundles and generalizations
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References:

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