Skoda–El Mir theorem

The Skoda–El Mir theorem is a theorem of complex geometry, stated as follows:

Theorem (Skoda, El Mir, Sibony). Let X be a complex manifold, and E a closed complete pluripolar set in X. Consider a closed positive current $\mathrm{\Theta }$ on $X\mathrm{\setminus }E$ which is locally integrable around E. Then the trivial extension of $\mathrm{\Theta }$ to X is closed on X.

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)

Template:Differential-geometry-stub