Let $X$ be a complex projective manifold of dimension $n$ and let $\mathcal E$ be an ample vector bundle of rank $r$. Let also $\tau = \tau (X, {\mathcal E}) = \min\{t \in {\mathbb R} : K_X + t \det {\mathcal E} {\rm \ is \ nef}\}$ be the nef value of the pair $(X, {\mathcal E})$. In this paper we classify the pairs $(X, {\mathcal E})$ such that $\tau (X, {\mathcal E}) \geq {n-2 \over r}$.
Manifolds polarized by vector bundles
NOVELLI, CARLA
2007
Abstract
Let $X$ be a complex projective manifold of dimension $n$ and let $\mathcal E$ be an ample vector bundle of rank $r$. Let also $\tau = \tau (X, {\mathcal E}) = \min\{t \in {\mathbb R} : K_X + t \det {\mathcal E} {\rm \ is \ nef}\}$ be the nef value of the pair $(X, {\mathcal E})$. In this paper we classify the pairs $(X, {\mathcal E})$ such that $\tau (X, {\mathcal E}) \geq {n-2 \over r}$.
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