Ballico, E. Spanned and ample vector bundles with low Chern numbers. (English) Zbl 0638.14010 Pac. J. Math. 140, No. 2, 209-216 (1989). 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 Cited in 4 Documents 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 Keywords:rank-2 ample vector bundle; ampleness; spanned vector bundle; Chern number PDFBibTeX XMLCite \textit{E. Ballico}, Pac. J. Math. 140, No. 2, 209--216 (1989; Zbl 0638.14010) Full Text: DOI