Monge-Ampère equations in big cohomology classes

Details Monge-Ampère equations in big cohomology classes Monge-Ampère equations in big cohomology classes

2008-12-18

arxiv.org/abs/0812.3674v2

Mathematics

Complex Variables

54 pages. Final version. To appear in Acta Math

Scientific paper

We define non-pluripolar products of closed positive currents on a compact Kaehler manifold. We show that a positive non-pluripolar measure can be written in a unique way as the top degree self-intersection (in the non-pluripolar sense) of a closed positive current in given big cohomology class. The solution is shown to have minimal singularities in the sense of Demailly if the measure is regular enough. These results are combined with a fixed point argument to construct singular Kaehler-Einstein volume forms with minimal singularities on varieties of general type.

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