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Apr 4, 2010 at 17:11 comment added Anton Geraschenko Thanks Georges. Looking over it now, it doesn't appear to say anything about reducibility of the general punctual Hilbert scheme, but I'll definitely look over it more carefully. This caught my eye: the last section shows irreducibility of the Hilbert scheme of fat points in the plane contained in the p-th infinitesimal neighborhood of the reduced point.
Apr 4, 2010 at 8:59 history answered Georges Elencwajg CC BY-SA 2.5