Symplectic spreads in \(PG(3,q)\), inversive planes and projective planes
type: Item
instance of: scholarly article
title: Symplectic spreads in \(PG(3,q)\), inversive planes and projective planes
zbMATH Open document ID: 0904.51001
DOI: 10.1016/S0012-365X(96)00345-7
published in: Discrete Mathematics
publication date: 1999-01-19T00:00:00Z
review text: This is a survey (without proofs) on the interrelation of the objects in the title of the paper. It contains the following information: connection between inversive planes and ovoids in \(\text{PG}(3, q)\); some important characterizations of classical inversive planes; projective and inversive planes of small order: uniqueness and existence; all known ovoids of \(\text{PG}(3,q)\) and of the quadric (generalized quadrangle) \(\text{Q}(4,q)\); existence and uniqueness of ovoids of the quadric \(\text{Q}(2n,q)\). Finally, there is a very interesting appendix on the equivalence of flocks of cones giving rise to translation generalized quadrangles, and a certain type of ovoids of \(\text{Q}(4,q)\) (and this is a new result, with an entirely geometric proof).
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 51E23
zbMATH DE Number: 1110041
zbMATH Keywords: spread
zbMATH Keywords: translation plane
zbMATH Keywords: survey
zbMATH Keywords: inversive planes
zbMATH Keywords: ovoids
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: generalized quadrangles
author: Joseph A. Thas
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1110041