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
Published electronically: December 20, 2011
MathSciNet review: 2957694
Full-text PDF

Abstract | References | Additional Information

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.

References [Enhancements On Off] (What's this?)

Additional Information

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

Received by editor(s): January 20, 2010
Received by editor(s) in revised form: May 29, 2010
Published electronically: December 20, 2011

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website