Effective non-vanishing conjectures for projective threefolds

Amäel Broustet; Andreas Höring

doi:10.1515/advgeom.2010.035

Published by De Gruyter August 10, 2010

Effective non-vanishing conjectures for projective threefolds

Amäel Broustet and Andreas Höring

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https://doi.org/10.1515/advgeom.2010.035

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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 pseudo-effective, 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.

Received: 2008-11-28

Revised: 2009-03-25

Published Online: 2010-08-10

Published in Print: 2010-October

Effective non-vanishing conjectures for projective threefolds

Abstract

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