Chen, Zhiyong; Deng, Fangfang On classification of higher-dimensional algebraic varieties with ample vector bundles. (Chinese. English summary) Zbl 1289.14005 Acta Math. Sin., Chin. Ser. 56, No. 2, 155-162 (2013). Summary: Let \(X\) be a smooth projective variety of dimension \(n(n \geq 3)\) and \(\mathcal{E}\) be an ample vector bundle with rank \(r=n-k(k\geq 1)\) over \(X\). We denote \(\Lambda(\mathcal{E}, K_X)=\max\{(-K_X-c_1(\mathcal{E}))\cdot C|R=\mathbb R_+[C]\in \Omega\), and \(l(R)=-K_X\cdot C\}\), where \(K_X\) is the canonical bundle of \(X,\;c_1(\mathcal{E})\) means the first Chern class of \(\mathcal{E},\;\Omega\) denotes the set of extremal rays \(R\) such that \((K_X+c_1(\mathcal{E}))\cdot C\leq 0,\;\mathbb R_+\) is the set of positive real number, and \(l(R)\) is the length of \(R\). The classification of \((X,\mathcal{E})\) is given when \(\Lambda(\mathcal{E}, K_X)\geq k-1\). MSC: 14J45 Fano varieties 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli Keywords:ample vector bundles; higher-dimensional algebraic varieties; numerically effective PDFBibTeX XMLCite \textit{Z. Chen} and \textit{F. Deng}, Acta Math. Sin., Chin. Ser. 56, No. 2, 155--162 (2013; Zbl 1289.14005)