Ovoids in infinite incidence structures
type: Item
instance of: scholarly article
title: Ovoids in infinite incidence structures
zbMATH Open document ID: 0816.51005
DOI: 10.1007/BF01198674
author: Peter J. Cameron
published in: Archiv der Mathematik
publication date: 1995-04-18T00:00:00Z
review text: Using simple transfinite induction, it is shown that a large class of infinite incidence structures (including polar spaces and most dual polar spaces, and generalized \(n\)-gons with \(n \geq 4\) and \(s= t\)) have the property that the point set can be partitioned into ovoids. As a result, there seems little hope of describing universal embeddings of these geometries in terms of hyperplanes. On the other hand, combined with a construction of Kantor, the result gives rise to large numbers of flat geometries with diagrams such as \(C_ 2 \cdot C_ 2\).
reviewed by: Peter J. Cameron
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51B05
zbMATH DE Number: 743521
zbMATH Keywords: flat geometries
zbMATH Keywords: Axiom of Choice
zbMATH Keywords: incidence structures
zbMATH Keywords: ovoids
zbMATH Keywords: universal embeddings
MaRDI profile type: Publication
cites work: Diagrams for geometries and groups
cites work: Q3733675
cites work: Buildings of spherical type and finite BN-pairs
full work available at URL: https://doi.org/10.1007/bf01198674
OpenAlex ID: W2086738612
description: scientific article; zbMATH DE number 743521