Singularities of the nested Hilbert scheme of points of length 3, 4
Abstract
We show that the projection morphism X[3,4] X[3] is flat even if it has reducible fiber. After analyzing blow-up constructions related to X[3,4], we conclude that X[3,4] has canonical Gorenstein singularities. As a corollary, we specify the singularities of several nested Hilbert schemes.
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