Skoda–El Mir theorem

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 $\Theta$ on $X\backslash E$ which is locally integrable around E. Then the trivial extension of $\Theta$ to X is closed on X.

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

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)

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[1] H. Skoda. Prolongement des courants positifs fermes de masse finie, Invent. Math., 66 (1982), 361–376.

[2] H. El Mir. Sur le prolongement des courants positifs fermes, Acta Math., 153 (1984), 1–45.

[3] N. Sibony, Quelques problemes de prolongement de courants en analyse complexe, Duke Math. J., 52 (1985), 157–197

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