Polynomial hulls and positive currents

Abstract

Let T be a positive plurisubharmonic current of bidimension (p,p) and let $\delta >0$. Assume that the Lelong number of T satisfies $\nu (T,a)\ge \delta$ on a dense subset of supp(T) (rectifiable currents satisfy this condition). Then $T=\varphi [X]$, where X is a complex subvariety of pure dimension p and $\varphi$ is a weakly plurisubharmonic function on X. We have an analogous result for plurisuperharmonic currents. We also introduce and study a notion of polynomial p-hull.

18 pages