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Effective non-vanishing conjectures for projective threefolds
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Amäel Broustet
Published/Copyright:
August 10, 2010
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.
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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Articles in the same Issue
- A combinatorial approach to Alexander–Hirschowitz's Theorem based on toric degenerations
- Triply periodic minimal surfaces which converge to the Hoffman–Wohlgemuth example
- Total absolute horospherical curvature of submanifolds in hyperbolic space
- The case of equality for an inverse Santaló functional inequality
- Circle configurations in strictly convex normed planes
- Rank four vector bundles without theta divisor over a curve of genus two
- Affine Tallini Sets and Grassmannians
- Geometry of self-dual flats over a PID on a polarity
- Logarithmic comparison theorem versus Gauss–Manin system for isolated singularities
- A kinematic formula for the total absolute curvature of intersections
- Reducible Veronese surfaces
- Effective non-vanishing conjectures for projective threefolds
