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On the reducibility of the postulation Hilbert scheme. (English) Zbl 1099.13029
Let $$H$$ be the Hilbert function of some $$0$$-dimensional subscheme of $$\mathbb P^n$$. The main result of this paper shows that, if the set of the sequences of Betti numbers compatible with $$H$$ has no minimum element, then the scheme $$\text{Hilb}^H(\mathbb P^n)$$ is reducible.

##### MSC:
 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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