New examples of finite \(\widetilde C_ 2\)-geometries
type: Item
instance of: scholarly article
title: New examples of finite \(\widetilde C_ 2\)-geometries
zbMATH Open document ID: 0780.51006
DOI: 10.1007/BF01264914
published in: Geometriae Dedicata
publication date: 1993-08-25T00:00:00Z
review text: The author constructs examples of finite \(\tilde C_ 2\)-geometries with parameters \(q+1,q-1,q+1\), where \(q\) is a power of 2. His construction starts with two hyperovals \({\mathcal O}\), \({\mathcal O}^*\) in a projective plane \(PG(2,q)\). The generalized quadrangles \(T^*_ 2({\mathcal O}^*)\) and \(T^*_ 2({\mathcal O})^{\text{dual}}\) appear as residues of the \(\tilde C_ 2\)-geometries. See also \textit{H. Van Maldeghem} [Mitt. Math. Semin. Giessen 189, 159 p. (1989; Zbl 0664.51004) and Geom. Dedicata 35, No. 1-3, 77-87 (1990; Zbl 0715.51003)].
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 205528
zbMATH Keywords: generalized quadrangles
zbMATH Keywords: hyperovals
Wikidata QID: Q56872296
author: Dmitrii V. Pasechnik
reviewed by: Theo Grundhöfer
MaRDI profile type: Publication
cites work: Q3851217
cites work: Q3733675
cites work: Q3344217
cites work: Generalized quadrangles with valuation
full work available at URL: https://doi.org/10.1007/bf01264914
OpenAlex ID: W268019011
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description: scientific article; zbMATH DE number 205528