Effective non-vanishing conjectures for projective threefolds

2008/11/19 by Broustet, Amaël, Höring, Andreas · 1 citation
#14J30 #14N30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0811.3059

Abstract

Let X be a smooth projective threefold, and let A be an ample line bundle such that K_X+A is nef. We show that if K_X or -K_X is pseudoeffective, the adjoint bundle K_X+A has global sections. We also give a very short proof of the Beltrametti-Sommese conjecture in dimension three, recently proven by Fukuma: if A is an ample line bundle such that K_X+2A is nef, the adjoint bundle K_X+2A has global sections.

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• Geometric effects of hyperbolic cohomology classes on Kähler manifolds (with an appendix by Benoît Claudon)

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