Polynomial hulls and positive currents

2002/06/28 by Tien‐Cuong Dinh, T. C. Dinh, Dinh, T. C.
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV

paper · pdf · doi:10.48550/arxiv.math/0206308

18 pages

openalex publication_date 2002/06/28 · arxiv created 2002/09/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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