Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

On a conjecture of Beltrametti and Sommese


Author: Andreas Höring
Journal: J. Algebraic Geom. 21 (2012), 721-751
DOI: https://doi.org/10.1090/S1056-3911-2011-00573-0
Published electronically: December 20, 2011
MathSciNet review: 2957694
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Abstract: Let $ X$ be a projective manifold of dimension $ n$. Beltrametti and
Sommese conjectured that if $ A$ is an ample divisor such that $ K_X+\linebreak (n-1)A$ is nef, then $ K_X+(n-1)A$ has non-zero global sections. We prove a weak version of this conjecture in arbitrary dimension. In dimension three, we prove the stronger non-vanishing conjecture of Ambro, Ionescu and Kawamata and give an application to Seshadri constants.


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Andreas Höring
Affiliation: Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu, Equipe de Topologie et Géométrie Algébrique, 175, rue du Chevaleret, 75013 Paris, France
Email: hoering@math.jussieu.fr

DOI: https://doi.org/10.1090/S1056-3911-2011-00573-0
Received by editor(s): January 20, 2010
Received by editor(s) in revised form: May 29, 2010
Published electronically: December 20, 2011

American Mathematical Society