A characterization of \({\mathbb{P}}_ n\) by vector bundles
type: Item
instance of: scholarly article
title: A characterization of \({\mathbb{P}}_ n\) by vector bundles
zbMATH Open document ID: 0726.14034
DOI: 10.1007/BF02571257
author: Thomas Peternell
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174189
review text: The following result [conjectured by \textit{S. Mukai}; cf. ``Open problems. Classification of algebraic and analytic manifolds'', Proc. Symp., Katata/Jap. 1982, Prog. Math. 39, 591-630 (1983; Zbl 0527.14002)] is proved: Theorem: Let X be a compact complex manifold of dimension n, E an ample vector bundle on X of rank \((n+1)\) satisfying \(c_ 1(E)=c_ 1(X)\). Then \(X\cong P_ n\) and \(E\cong {\mathcal O}_{P_ n}(1)^{n+1}.\) The cases \(n\leq 2\) are clear. Mukai proved the case \(n=3\).
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 4198193
zbMATH Keywords: characterization of projective space
zbMATH Keywords: first Chern class
zbMATH Keywords: extremal rational curves
zbMATH Keywords: ample vector bundle
reviewed by: O. Păsărescu
MaRDI profile type: Publication
cites work: Q3338372
cites work: Generalized adjunction and applications
cites work: Q3825176
cites work: Threefolds whose canonical bundles are not numerically effective
cites work: Vector bundles on complex projective spaces
cites work: Length of extremal rays and generalized adjunction
cites work: Characterizations of complex projective spaces and hyperquadrics
cites work: Projective manifolds with ample tangent bundles
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description: scientific article; zbMATH DE number 4198193