On Lelong Numbers of Positive Closed Currents on ℙⁿ

2017/09/29 by James J. Heffers, Heffers, James J.
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1709.10502

openalex publication_date 2017/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a positive closed current of bidimension (p,p) with unit mass on the complex projective space \mathbb Pⁿ. For certain values of α and β= β(p, α) we show that if T has enough points where the Lelong number is at least α, then the upper level set E_β⁺ (T) of points where T has Lelong number strictly larger than β has certain geometric properties.

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