Nefness of adjoint bundles for ample vector bundles of corank 3

Details Nefness of adjoint bundles for ample vector bundles of corank 3 Nefness of adjoint bundles for ample vector bundles of corank 3

2011-08-23

arxiv.org/abs/1108.4489v1

Mathematics

Algebraic Geometry

31 pages

Scientific paper

Let $\mathcal{E}$ be an ample vector bundle of rank $r\geq 2$ on a smooth
complex projective variety $X$ of dimension $n$. The aim of this paper is to
describe the structure of pairs $(X,\mathcal{E})$ as above whose adjoint
bundles $K_X+\det\mathcal{E}$ are not nef for $r=n-3$. Furthermore, we give
some immediate consequences of this result in adjunction theory.

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