Skoda–El Mir theorem
The Skoda–El Mir theorem is a theorem of complex geometry, stated as follows:
Theorem (Skoda, El Mir, Sibony ). Let X be a complex manifold, and E a closed complete pluripolar set in X. Consider a closed positive current on which is locally integrable around E. Then the trivial extension of to X is closed on X.
- 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
- 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)