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Manifolds polarized by vector bundles. (English) Zbl 1222.14091
Summary: Let \(X\) be a complex projective manifold of dimension \(n\) and let \(\mathcal E\) be an ample vector bundle of rank \(r\). Let also \(\tau = \tau(X,\mathcal E) = \min \{t\in\mathbb{R}: K_X + t \det \mathcal E \text{ is nef}\}\) be the nef value of the pair \((X,\mathcal E)\). In this paper we classify the pairs \((X,\mathcal E)\) such that \(\tau(X,\mathcal E)\geq \frac{n-2}{r}\).

MSC:
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14J40 \(n\)-folds (\(n>4\))
14E30 Minimal model program (Mori theory, extremal rays)
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