  Using the notion of equivariant Kirwan map, as defined by Goldin, we prove
that -- in the case of Hamiltonian torus actions with isolated fixed points --
Tolman and Weitsman's description of the kernel of the Kirwan map can be
deduced directly from the residue theorem of Jeffrey and Kirwan. A
characterization of the kernel of the Kirwan map in terms of residues of one
variable (i.e. associated to Hamiltonian circle actions) is obtained.
