Inequidimensionality of Hilbert schemes

Chang, Mei-Chu

doi:10.1090/S0002-9939-97-03836-7

Inequidimensionality of Hilbert schemes
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Proc. Amer. Math. Soc. 125 (1997), 2521-2526 Request permission

Abstract:

We give a lower bound on the number of distinct dimensions of irreducible components of the Hilbert scheme of codimension 2 subvarieties in $\mathbb {P}^{n}$, for $n \le 5$ (respectively, the moduli space of surfaces or 3-folds) in terms of the Hilbert polynomial (resp. Chern numbers).

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