On a conjecture of Beltrametti and Sommese

Details On a conjecture of Beltrametti and Sommese On a conjecture of Beltrametti and Sommese

2009-12-07

arxiv.org/abs/0912.1295v2

Mathematics

Algebraic Geometry

23 pages, major revision: fixed a gap in the proof and made many modifications

Scientific paper

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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