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 νa, 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 νa, 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: νz, ψ(φ)≥c} where c>0, are in fact analytic sets, provided that the weightψ satisfies some additional conditions.
Citation
Aron Lagerberg. "A new generalization of the Lelong number." Ark. Mat. 51 (1) 125 - 156, April 2013. https://doi.org/10.1007/s11512-011-0158-0
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