The Skoda–El Mir theorem is a theorem of
complex geometry
In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and c ...
,
stated as follows:
Theorem (
Skoda
Škoda means ''pity'' in the Czech and Slovak languages. It may also refer to:
Czech brands and enterprises
* Škoda Auto, automobile and previously bicycle manufacturer in Mladá Boleslav
** Škoda Motorsport, the division of Škoda Auto respons ...
, 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, 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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