  In this paper, we extract natural invariants of a singularity by using the
Deligne weight filtration on the cohomology of an exceptional fibre of a
resolution, and also on the intersection cohomology of the link. Our primary
goal is to study and give natural bounds on the weights in terms of direct
images of differential forms. These bounds can be made explicit for various
standard classes such as rational, isolated normal Cohen-Macaulay and toroidal
singularities, and lead to strong restrictions on the topology of these
singularities. A secondary goal of this paper is to make the weight filtration,
and related constructions, more widely accessible. So we have tried to make the
presentation somewhat self contained. This is supersedes our earlier preprint
arXiv:0902.4234.
