Let
(
C
,
t
)
(C,\mathbf {t})
(
t
=
(
t
1
,
…
,
t
n
)
\mathbf {t}=(t_1,\ldots ,t_n)
) be an
n
n
-pointed smooth projective curve of genus
g
g
and take an element
λ
=
(
λ
j
(
i
)
)
∈
C
n
r
\boldsymbol {\lambda }=(\lambda ^{(i)}_j)\in \mathbf {C}^{nr}
such that
−
∑
i
,
j
λ
j
(
i
)
=
d
∈
Z
-\sum _{i,j}\lambda ^{(i)}_j=d\in \mathbf {Z}
. For a weight
α
\boldsymbol {\alpha }
, let
M
C
α
(
t
,
λ
)
M_C^{\boldsymbol {\alpha }}(\mathbf {t},\boldsymbol {\lambda })
be the moduli space of
α
\boldsymbol {\alpha }
-stable
(
t
,
λ
)
(\mathbf {t},\boldsymbol {\lambda })
-parabolic connections on
C
C
and let
R
P
r
(
C
,
t
)
a
RP_r(C,\mathbf {t})_{\mathbf {a}}
be the moduli space of representations of the fundamental group
π
1
(
C
∖
{
t
1
,
…
,
t
n
}
,
∗
)
\pi _1(C\setminus \{t_1,\ldots ,t_n\},*)
with the local monodromy data
a
\mathbf {a}
for a certain
a
∈
C
n
r
\mathbf {a}\in \mathbf {C}^{nr}
. Then we prove that the morphism
R
H
:
M
C
α
(
t
,
λ
)
→
R
P
r
(
C
,
t
)
a
\mathbf {RH}:M_C^{\boldsymbol {\alpha }}(\mathbf {t},\boldsymbol {\lambda })\rightarrow RP_r(C,\mathbf {t})_{\mathbf {a}}
determined by the Riemann-Hilbert correspondence is a proper surjective bimeromorphic morphism. As a corollary, we prove the geometric Painlevé property of the isomonodromic deformation defined on the moduli space of parabolic connections.