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can $E_c(T)={x\in X~:~\nu(T,x)\geq c}$ have isolated point? where T is a positive current of bidegree 1, c is a positive real number, $X$ is a complex variety, and $\nu(T,x)$ is the Lelong number of T on x.

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What is $E_c(T)?$ –  Igor Rivin Nov 29 '11 at 19:35

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$E_c(T)=(x\in X~:~\nu(T,x)\geq c)$

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You can edit your own question ;) –  Jesus Martinez Garcia Jan 3 '12 at 23:45

Yes, it can. For example take $X=\mathbb{C}$ and $T=dd^c\log |z|^2$ (up to a positive factor this is the delta function at the origin), then $T$ has positive Lelong number at the origin (with the correct normalization the Lelong number is $1$) and zero outside.

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