DOI: 10.5802/aif.3805 ISSN: 0373-0956
On Lelong numbers of plurisubharmonic functions on complex spaces
Le Mau Hai, Pham Hoang Hiep, Trinh Tung
In this paper, we introduce the notion of strong locally irreducible complex spaces
X
. Based on this notion we prove the equality
ν
¯
φ
(
x
)
=
mult
(
X
,
x
)
.
ν
φ
(
x
)
for all
x
∈
X
, where
ν
¯
φ
(
x
)
is the projective mass of a plurisubharmonic function
φ
at
x
and
mult
(
X
,
x
)
is the multiplicity of
X
at
x
and
ν
φ
(
x
)
is Lelong number of
φ
at
x
. Moreover, we show that the closure of the upper-level sets
{
z
∈
X
:
ν
φ
(
z
)
≥
c
}
of a plurisubharmonic function
φ
on a strong locally irreducible complex space
X
is a subvariety of
X
for all
c
≥
0
.