2.4 Extension of Kähler currents [00TB]

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2.4 Extension of Kähler currents

Extension theorems allow us to think extrinsically about Kähler currents on subvarieties in some ambient projective manifold.

Theorem 2.13.

([11, Thm. B]) Let $(X,\omega)$ be a projective manifold with a Kähler form representing an integral class, and $Y$ be a smooth subvariety of $X$ . Then any $\phi\in PSH(Y,\omega|_{Y})$ extends to $\phi\in PSH(X,\omega)$ .