The Euler characteristic of tautological sheaves on singular Hilbert schemes of points

There were many computations of the Euler characteristic of the tautological sheaves on Hilbert scheme of points on surfaces. In higher dimensions the Hilbert schemes of points are in general singular, and very few results were known. We use Thomason's localization theorem to do some computations on Hilbert schemes of points on topic 3-folds. We need to study the local structure of these Hilbert schemes. As a by product, we show that the Hilbert scheme of less than 8 points on a smooth 3-fold has only normal, Gorenstein and rational singularities.