On the classification of non-normal cubic hypersurfaces
type: Item
instance of: scholarly article
title: On the classification of non-normal cubic hypersurfaces
zbMATH Open document ID: 1225.14044
author: Wanseok Lee
author: Euisung Park
author: Peter Schenzel
published in: Journal of Pure and Applied Algebra
publication date: 2011-05-10T00:00:00Z
review text: The main results of this article deal with non-normal, projective, cubic hypersurfaces over an algebraically closed field \(K\). If the ambient projective space has dimension at least \(5\), then such a hypersurface is necessarily a cone (which follows from results proved elsewhere). Thus the problem of determining the projective equivalence classes of such hypersurfaces reduces to the one in \(4\) or lower dimensional projective spaces over \(K\). In Theorem 3.1 of the article, authors provide a list of explicit canonical equations of (non-normal, projective, cubic) hypersurfaces corresponding to the distinct projective equivalence classes. As to be expected, when \(K\) has characteristic \(2\) or \(3\) there are more classes. The authors' proof proceeds via a detailed description of the normalization of the hypersurfaces defined by the canonical equations. The ensuing classification is asserted in Theorem 4.2. Normalization is used only to establish the projective inequivalence of the equations listed in Theorem 3.1.
Mathematics Subject Classification ID: 14N15
Mathematics Subject Classification ID: 51N35
zbMATH DE Number: 5886360
zbMATH Keywords: projective
zbMATH Keywords: cubic
zbMATH Keywords: hypersurfaces
MaRDI profile type: Publication
full work available at URL: j.jpaa.2010.12.007
OpenAlex ID: W1980030455
cites work: Arithmetic properties of projective varieties of almost minimal degree
cites work: On the Classification of Cubic Surfaces
cites work: Q3995221
cites work: Q4517585
DOI: 10.1016/J.JPAA.2010.12.007
description: scientific article; zbMATH DE number 5886360