On a conjecture of Beltrametti and Sommese

2009/12/07 by Höring, Andreas · 1 citation
#14C17 #14C20 #14C40 #14E30 #14J40 #14N30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0912.1295

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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