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The Skoda–El Mir theorem is a theorem of
complex geometry In mathematics, complex geometry is the study of geometry, geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of space (mathematics), spaces su ...
, stated as follows: Theorem ( Skoda, El Mir, SibonyN. Sibony, ''Quelques problemes de prolongement de courants en analyse complexe,'' Duke Math. J., 52 (1985), 157–197). Let ''X'' be a
complex manifold In differential geometry and complex geometry, a complex manifold is a manifold with a ''complex structure'', that is an atlas (topology), atlas of chart (topology), charts to the open unit disc in the complex coordinate space \mathbb^n, such th ...
, 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


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)
' Complex manifolds Several complex variables Theorems in geometry {{differential-geometry-stub