Non-obstructedness of Gorenstein subschemes of codimension 3 in \(\mathbb{P}{}^ n\)
A closed subscheme of \(\mathbb{P}^ n\) is called non-obstructed if the corresponding point of the Hilbert scheme \(H=\text{Hilb}^ n_{p(t)}\) which parametrizes closed subschemes of \(\mathbb{P}^ n\) with Hilbert polynomial \(p(t)\in\mathbb{Q}(t)\) is nonsingular. \textit{G. Ellingsrud} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 8 (1975), 423-432 (1976; Zbl 0325.14002)] proved that arithmetically Cohen-Macaulay closed subschemes of codimension 2 in \(\mathbb{P}^ n\) are non-obstructed. The author shows that Gorenstein subschemes of codimension 3 in \(\mathbb{P}^ n\) are parametrized by an open, nonsingular subset of the corresponding Hilbert scheme. Finally, the almost complete intersection closed subschemes of codimension 3 are shown to be nonobstructed.
scientific article; zbMATH DE number 95936