Monge-Ampère operators, Lelong numbers and intersection theory. (English) Zbl 0792.32006

Demailly, Jean-Pierre

Ancona, Vincenzo (ed.) et al., Complex analysis and geometry. New York: Plenum Press. The University Series in Mathematics. 115-193 (1993).

This article is a survey on the theory of Lelong numbers, viewed as a tool for studying intersection theory by complex differential geometry. The paper contains earlier works of the author [Mém. Soc. Math. Fr., Nouv. Sér. 19, 124 p. (1985; Zbl 0579.32012) and Acta Math. 159, 153- 169 (1987; Zbl 0629.32011)] and of Y. T. Siu [Invent. Math. 27, 53- 156 (1974; Zbl 0289.32003)]. Many results are given with complete proofs, which are shorter and simpler than the original ones. The references contain 37 items on these topics.
For the entire collection see [Zbl 0772.00007].

Reviewer: E.Outerelo (Madrid)

MSC:

32C30	Integration on analytic sets and spaces, currents
32W20	Complex Monge-Ampère operators
32U05	Plurisubharmonic functions and generalizations

Keywords:

Monge-Ampère operators; current; plurisubharmonic functions; Lelong numbers; intersection theory

Citations:

Zbl 0579.32012; Zbl 0629.32011; Zbl 0289.32003