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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)
##### Keywords:
Ample vector bundle; Extremal rays; Adjunction theory
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##### References:
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