A classification of non-degenerate homogeneous equiaffine hypersurfaces in four complex dimensions
type: Item
instance of: scholarly article
title: A classification of non-degenerate homogeneous equiaffine hypersurfaces in four complex dimensions
zbMATH Open document ID: 1022.53043
published in: The Asian Journal of Mathematics
publication date: 2002-10-22T00:00:00Z
review text: An equiaffine transformation of \(\mathbb{C}^n\) is a map of type \(V \mapsto Av+b\), where \(A\in SL(h,\mathbb{C})\) and \(b\in\mathbb{C}^n\). An equiaffine homogeneous hypersurface of \(\mathbb{C}^n\) is a complex hypersurface \(\Sigma\subset \mathbb{C}^n\) which is the orbit of a complex Lie subgroup of the group of all equiaffine transformations. Such surfaces in \(\mathbb{C}^3\) were classified by \textit{K. Nomizu} and \textit{T. Sasaki} in [Manuscr. Math. 73, 39-44 (1991; Zbl 0753.53008)]. In the paper under review, the corresponding classification problem is solved for non-degenerate hypersurfaces of \(\mathbb{C}^n\). These hypersurfaces are explicitly described via equations and computable invariants are found which distinguish between different non-equivalent hypersurfaces.
reviewed by: Giovanni Calvaruso
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1818551
zbMATH Keywords: homogeneous equiaffine hypersurfaces
zbMATH Keywords: orbit
zbMATH Keywords: complex Lie subgroup
author: M. Eastwood
author: Vladimir Ejov
MaRDI profile type: Publication
full work available at URL: ajm.2001.v5.n4.a7
OpenAlex ID: W2652334552
DOI: 10.4310/AJM.2001.V5.N4.A7
description: scientific article; zbMATH DE number 1818551