Skoda–El Mir theorem
From HandWiki
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 [math]\displaystyle{ \Theta }[/math] on [math]\displaystyle{ X \backslash E }[/math] which is locally integrable around E. Then the trivial extension of [math]\displaystyle{ \Theta }[/math] 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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