On a conjecture of Beltrametti and SommeseOn a conjecture of Beltrametti and Sommese

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 Author Höring, Andreas Source arXiv.org Content type Text File Format PDF Date of Submission 2009-12-07 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Algebraic Geometry ♦ 14C17 ♦ 14C40 ♦ 14C20 ♦ 14J40 ♦ 14N30 ♦ math 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. Educational Use Research Learning Resource Type Article