The Singularities of the Principal Component of the Hilbert Scheme of Points
نویسنده
چکیده
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 d, n ≥ 1. In particular, his conjecture implies that the principal component of Hilb(Cd) is Cohen-Macaulay (see [11, Section 5.2] and [17, Conjecture 18.38]).
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