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,
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 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 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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