Skoda-El Mir theorem

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

Theorem (Skoda ^[1], El Mir ^[2], Sibony ^[3]). Let X be a complex manifold, and E a closed complete pluripolar set in X. Consider a closed positive current $Θ$ on $X \backslash E$ which is locally integrable around E. Then the trivial extension of $Θ$ to X is closed on X.

[edit] References

J.-P. Demailly, 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)

[edit] Notes

^ H. Skoda. Prolongement des courants positifs fermes de masse finie, Invent. Math., 66 (1982), 361-376.
^ H. El Mir. Sur le prolongement des courants positifs fermes, Acta Math., 153 (1984), 1-45.
^ N. Sibony, Quelques problemes de prolongement de courants en analyse complexe, Duke Math. J., 52 (1985), 157-197