  We construct complete Kahler metrics of Saper type on the nonsingular set of
a subvariety X of a compact Kahler manifold using (a) a method for replacing a
sequence of blow-ups along smooth centers, used to resolve the singularities of
X, with a single blow-up along a product of coherent ideals corresponding to
the centers and (b) an explicit local formula for a Chern form associated to
this single blow-up. Our metrics have a particularly simple local formula,
involving essentially a product of distances to the centers of the blow-ups
used to resolve the singularities of X. Our proof of (a) uses a generalization
of Chow's theorem for coherent ideals, proved using the Direct Image Theorem.
