A new generalization of the Lelong number
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...
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| Published in | Arkiv för matematik Vol. 51; no. 1; pp. 125 - 156 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.04.2013
|
| Subjects | |
| Online Access | Get full text |
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| Summary: | 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. |
|---|---|
| ISSN: | 0004-2080 1871-2487 1871-2487 |
| DOI: | 10.1007/s11512-011-0158-0 |