Effective non-vanishing conjectures for projective threefolds

Details Effective non-vanishing conjectures for projective threefolds Effective non-vanishing conjectures for projective threefolds

2008-11-19

arxiv.org/abs/0811.3059v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

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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