Siu's semicontinuity theorem

In complex analysis, the Siu semicontinuity theorem implies that the Lelong number of a closed positive current on a complex manifold is semicontinuous. More precisely, the points where the Lelong number is at least some constant form a complex subvariety. This was conjectured by Harvey & King (1972) and proved by Siu. Demailly (1987) generalized Siu's theorem to more general versions of the Lelong number.

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