  We present a restricted version of some affine Jacobi's residue formula (on
an affine algebraic variety) with applications to higher dimensional (and
affine) analogues of Wood's (or Reiss's) relations about the interpolation of
pieces of analytic manifolds. We also compare algebraic and analytic
constructions of residue currents along analytic cycles and sketch some of
their main properties. This work extend previous work of the authors in the
affine space.
