  We introduce a new type of pluricomplex Green function which has a
logarithmic pole along a complex subspace A of a complex manifold X. It is the
largest negative plurisubharmonic function on X whose Lelong number is at least
the Lelong number of log max{|f_1|,...,|f_m|}, where f_1,...,f_m are local
generators for the ideal sheaf of A. The pluricomplex Green function with a
single logarithmic pole or a finite number of weighted poles is a very special
case of our construction. We give several equivalent definitions of this
function and study its properties, including boundary behaviour, continuity,
and uniqueness. This is based on and extends our previous work on disc
functionals and their envelopes.
