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arXiv · 0912.1295

On a conjecture of Beltrametti and Sommese

Andreas Höring
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Abstract

Let X be a projective manifold of dimension n. Beltrametti and Sommese conjectured that if A is an ample divisor such that $K_X+(n-1)A$ is nef, then $K_X+(n-1)A$ has non-zero global sections. We prove a weak version of this conjecture in arbitrary dimension. In dimension three, we prove the stronger non-vanishing conjecture of Ambro, Ionescu and Kawamata and give an application to Seshadri constants.

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Andreas Höring. 2009-12-07. On a conjecture of Beltrametti and Sommese. https://arxiv.org/abs/0912.1295

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