  We give a factorization of the fundamental cycle of an analytic space in
terms of certain differential forms and residue currents associated with a
locally free resolution of its structure sheaf. Our result can be seen as a
generalization of the classical Poincar\'e-Lelong formula. It is also a current
version of a result by Lejeune-Jalabert, who similarly expressed the
fundamental class of a Cohen-Macaulay analytic space in terms of differential
forms and cohomological residues.
