In [11], Haiman proved the remarkable result that the isospectral Hilbert scheme of points in the plane is normal, Cohen-Macaulay and Gorenstein. He also showed that this implies the n! conjecture and the positivity conjecture for the Kostka-Macdonald coefficients. In addition, he conjectured that the isospectral Hilbert scheme over the principal component of Hilb(Cd) is Cohen-Macaulay for any ...