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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.

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