The embedding in \(\text{AG}(3,q)\) of \((0,2)\)-geometries with no planar nets
type: Item
instance of: scholarly article
title: The embedding in \(\text{AG}(3,q)\) of \((0,2)\)-geometries with no planar nets
zbMATH Open document ID: 1063.51005
published in: Journal of Combinatorial Theory. Series A
publication date: 2005-02-22T00:00:00Z
review text: A \((0,\alpha)\)-geometry \(S=({\mathcal P},{\mathcal B},I)\) is a connected linear space of order \((s,t)\) with the property that for every anti-flag \((P,L)\) the number \(\alpha(p,L)\) of lines of \(S\) through \(P\) intersecting \(L\) is equal to \(0\) or a constant \(\alpha\). In the paper under review, the author studies \((0,2)\)-geometries of order \((2^h-1,t)\) embedded in AG\((3,2^h)\) with no planar nets. Assuming \(t=2^h\), the author provides a complete classification.
reviewed by: Antonio Cossidente
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 2136709
zbMATH Keywords: affine embeddings
zbMATH Keywords: full embedding
zbMATH Keywords: planar oval set
author: Nikias de Feyter
MaRDI profile type: Publication
full work available at URL: j.jcta.2004.06.012
OpenAlex ID: W1969416925
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DOI: 10.1016/J.JCTA.2004.06.012
description: scientific article; zbMATH DE number 2136709