Geometric hyperplanes of non-embeddable Grassmannians
type: Item
instance of: scholarly article
title: Geometric hyperplanes of non-embeddable Grassmannians
zbMATH Open document ID: 0777.51002
published in: European Journal of Combinatorics
publication date: 1993-05-16T00:00:00Z
review text: The author gives a complete classification of geometric hyperplanes for Grassmann spaces arising from the \(k\)-dimensional subspaces of a vector space \(V\) over a proper skew field. (Such a Grassmann space is not embeddable in a projective space.) Every geometric hyperplane is formed by all \(k\)-subspaces that meet a subspace of codimension \(k\) nontrivially. Hence to within projective transformations there is just a unique type of geometric hyperplane. This is in sharp contrast to geometric hyperplanes of Grassmann spaces over a commutative field. They arise as hyperplane sections of the associated Grassmann variety [the reviewer, J. Geom. 16, 168-180 (1982; Zbl 0463.51004), the second author, J. Algebra 145, No. 1, 55-82 (1992; Zbl 0751.51002)] and are not in one orbit with respect to the projective group.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51M35
zbMATH DE Number: 167693
zbMATH Keywords: geometric hyperplanes
zbMATH Keywords: Grassmann spaces
author: J. I. Hall
author: E. E. Shult
MaRDI profile type: Publication
full work available at URL: eujc.1993.1005
OpenAlex ID: W2046422074
DOI: 10.1006/EUJC.1993.1005
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description: scientific article; zbMATH DE number 167693