Abstract
Abstract Let X be a smooth projective threefold, and let A be an ample line bundle such that KX + A is nef. We show that if KX or –KX is pseudo-effective, the adjoint bundle KX + 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 KX + 2A is nef, the adjoint bundle KX + 2A has global sections.
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