Monge-Amp\`ere equations in big cohomology classes

Autor:	Boucksom, S., Eyssidieux, P., Guedj, V., Zeriahi, A.
Rok vydání:	2008
Předmět:	Mathematics - Complex Variables Mathematics - Differential Geometry 32U05 (primary) 35D05 35D10 (secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 54 pages. Final version. To appear in Acta Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0812.3674 Zobrazit plný text záznamu View this record from Arxiv