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Licensed Unlicensed Requires Authentication Published by De Gruyter August 10, 2010

Effective non-vanishing conjectures for projective threefolds

  • Amäel Broustet and Andreas Höring
From the journal


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.

Received: 2008-11-28
Revised: 2009-03-25
Published Online: 2010-08-10
Published in Print: 2010-October

© de Gruyter 2010

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