Polynomial hulls and positive currents

الأصل · EN

Let T be a positive plurisubharmonic current of bidimension (p,p) and let δ>0. Assume that the Lelong number of T satisfies ν(T,a)≥ δ on a dense subset of supp(T) (rectifiable currents satisfy this condition). Then T=ϕ[X], where X is a complex subvariety of pure dimension p and ϕ 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.