Effective non-vanishing conjectures for projective threefolds

Amaël Broustet; Andreas Höring

paper

Effective non-vanishing conjectures for projective threefolds

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 $K_{X} + 2 A$ is nef, the adjoint bundle $K_{X} + 2 A$ has global sections.

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