On the volume of a line bundle

Details On the volume of a line bundle On the volume of a line bundle

2002-01-05

arxiv.org/abs/math/0201031v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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