  We study properties of a Green function G_A with singularities along a
complex subspace A of a complex manifold X. It is defined as the largest
negative plurisubharmonic function u satisfying locally u\leq \log|\psi|+C,
where \psi=(\psi_1, ...,\psi_m), \psi_1, ...,\psi_m are local generators for
the ideal sheaf I_A of A, and C is a constant depending on the function u and
the generators. A motivation for this study is to estimate global bounded
functions from the sheaf I_A and thus proving a ``Schwarz Lemma'' for I_A.
