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Spanned and ample vector bundles with low Chern numbers. (English) Zbl 0638.14010

Let X be a complete variety, \(\dim (X)=2r+e\), \(e=0\) or 1. Assume either X locally Cohen-Macaulay or of characteristic \(0.\) Let E be a rank-2 ample vector bundle on X, E generated by global sections. Assume \(c_ 2(E)\) \(rc_ 1(E)\) \(e=2\) e. Here we prove using geometric constructions that \(X\cong {\mathbb{P}}^{2r+e}.,\quad E=2{\mathcal O}_{{\mathbb{P}}^{2r+e}}(1)\). For related work (using Mori theory) see the works of Wisniewski quoted in the paper.
Reviewer: E.Ballico

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14N05 Projective techniques in algebraic geometry
57R20 Characteristic classes and numbers in differential topology
14C20 Divisors, linear systems, invertible sheaves
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