A new generalization of the Lelong number |
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Authors: | Aron Lagerberg |
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Institution: | 1. Department of Mathematics, Chalmers University of Technology and University of G?teborg, SE-412 96, G?teborg, Sweden
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Abstract: | We will introduce a quantity which measures the singularity of a plurisubharmonic function φ relative to another plurisubharmonic function ψ, at a point a. We denote this quantity by ν a,ψ (φ). It can be seen as a generalization of the classical Lelong number in a natural way: if ψ=(n?1)log|????a|, where n is the dimension of the set where φ is defined, then ν a,ψ (φ) coincides with the classical Lelong number of φ at the point a. 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:ν z,ψ (φ)≥c} where c>0, are in fact analytic sets, provided that the weight ψ satisfies some additional conditions. |
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