Non-obstructedness of Gorenstein subschemes of codimension 3 in \(\mathbb{P}{}^ n\)
type: Item
instance of: scholarly article
title: Non-obstructedness of Gorenstein subschemes of codimension 3 in \(\mathbb{P}{}^ n\)
zbMATH Open document ID: 0766.14001
published in: Beiträge zur Algebra und Geometrie
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/138511
review text: 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.
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14M07
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 95936
zbMATH Keywords: non-obstructed subscheme
zbMATH Keywords: Gorenstein subschemes of codimension
zbMATH Keywords: Hilbert scheme
zbMATH Keywords: almost complete intersection
author: Rosa M. Miró-Roig
reviewed by: Cristodor-Paul Ionescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 95936