2010/01/20 by Aron Lagerberg, Lagerberg, Aron
Mathematics · #32S05 #32U05 #32U25 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #msc:32S05 #msc:32U05 #msc:32U25
paper · pdf · doi:10.48550/arxiv.1001.3562
29 pages
arxiv created 2010/01/20 · openalex publication_date 2010/01/20 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a quantity which measures the singularity of a plurisubharmonic function f relative to another plurisubharmonic function g, at a point a. This quantity, which we denote by νa,g(f), can be seen as a generalization of the classical Lelong number, in a natural way. The main theorem of this article says that the upper level sets of our generalized Lelong number, i.e. the sets of the form \z: νz,g(f) ≥ c > 0 \, are in fact analytic sets, under certain conditions on the weight g.