Skoda-El Mir theorem

The Skoda-El Mir theorem is a theorem of complex geometry, stated as follows:

Theorem (Skoda [H. Skoda. "Prolongement des courants positifs fermes de masse finie", Invent. Math., 66 (1982), 361-376.] , El Mir [H. El Mir. "Sur le prolongement des courants positifs fermes", Acta Math., 153 (1984), 1-45.] , Sibony [N. Sibony, "Quelques problemes de prolongement de courants en analyse complexe," Duke Math. J., 52 (1985), 157-197] ). Let "X" be a complex manifold, and "E" a closed complete pluripolar set in "X". Consider a closed positive current $Theta$ on which is locally integrable around "E". Then the trivial extension of $Theta$ to "X" is closed on "X".

References

*J.-P. Demailly," [http://arxiv.org/abs/alg-geom/9410022 L² vanishing theorems for positive line bundles and adjunction theory, Lecture Notes of a CIME course on "Transcendental Methods of Algebraic Geometry" (Cetraro, Italy, July 1994)] "

Notes