PSEUDO-EFFECTIVE LINE BUNDLES ON COMPACT KÄHLER MANIFOLDS

By J. Demailly, T. Peternell, Michael Schneider. 2000

227 citations recorded by the source corpus.

The goal of this work is to pursue the study of pseudo-effective line bundles and vector bundles. Our first result is a generalization of the Hard Lefschetz theorem for cohomology with values in a pseudo-effective line bundle. The Lefschetz map is shown to be surjective when (and, in general, only when) the pseudo-effective line bundle is twisted by its multiplier ideal sheaf. This result has several geometric applications, e.g. to the study of compact Kahler manifolds with pseudo-effective canonical or anti-canonical line bundles. Another concern is to understand pseudo-effectivity in more algebraic terms. In this direction, we introduce the concept of an "almost" nef line bundle, and mean by this that the degree of the bundle is nonnegative on sufficiently generic curves. It can be shown that pseudo-effective line bundles are almost nef, and our hope is that the converse also holds true. This can be checked in some cases, e.g. for the canonical bundle of a projective 3-fold. From this, we derive some geometric properties of the Albanese map of compact Kahler 3-folds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21467132d406c2408804b24221fddbfa850151e2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On regularization of plurisubharmonic functions on manifolds (2007, methodology): “Guedj and Zeriahi [6] used complicated methods developed by Demailly (see [2], [4], [5]) to show that such an approximation is possible when M admits a positive holomorphic line bundle.”