The Skoda–El Mir theorem is a theorem of
complex geometry,
stated as follows:
Theorem (
Skoda, El Mir,
Sibony[N. 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 an atlas of charts to the open unit disc in \mathbb^n, such that the transition maps are holomorphic.
The term complex manifold is variously used to mean a com ...
, 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''.
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
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