On the volume of a line bundle
Algebraic Geometry
2007-05-23 v1 Complex Variables
Abstract
Using a result of Fujita on approximate Zariski decompositions and the singular version of Demailly's holomorphic Morse inequalities as obtained by Bonavero, we express the volume of a line bundle in terms of the absolutely continuous parts of all the positive curvature currents on it, with a way to pick an element among them which is most homogeneous with respect to the volume. This enables us to introduce the volume of any pseudoeffective class on a compact Kaehler manifold, and Fujita's theorem is then extended to this context.
Cite
@article{arxiv.math/0201031,
title = {On the volume of a line bundle},
author = {Sebastien Boucksom},
journal= {arXiv preprint arXiv:math/0201031},
year = {2007}
}