From semifield flocks to the generalized translation dual of a semifield (Q1700421)
From MaRDI portal
| This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: From semifield flocks to the generalized translation dual of a semifield |
scientific article; zbMATH DE number 6847113
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | From semifield flocks to the generalized translation dual of a semifield |
scientific article; zbMATH DE number 6847113 |
Statements
From semifield flocks to the generalized translation dual of a semifield (English)
0 references
5 March 2018
0 references
\textit{J. A. Thas} [J. Comb. Theory, Ser. A 79, No. 2, 223--254 (1997; Zbl 0887.51004)] developed relationships between translation generalized quadrangles and symplectic semifield spreads. Sometimes, there are interesting and important links between geometrical objects. For instance, \textit{J. A. Thas} [Eur. J. Comb. 8, 441--452 (1987; Zbl 0646.51019)] proved that given a flock \({\mathcal F}\) of a quadratic cone of \(\mathrm{PG}(3,q)\), then there can be a generalized quadrangle \(Q({\mathcal F})\) associated to this flock \({\mathcal F}\). This means that new results on one of the geometrical objects can lead to new results on the other geometrical objects. This article discusses these relationships between translation generalized quadrangles and symplectic semifield spreads, and discusses some open problems. The discussed topics include: translation ovoids of \(Q(4,q)\) and semifield flocks, translation ovoids of the Klein quadric \(Q^+(5,q)\), geometric spread sets and semifields, and generalized translation dual of a semifield.
0 references
ovoids
0 references
semifield flocks
0 references
translation generalized quadrangles
0 references
symplectic semifield spreads
0 references
geometric spread sets
0 references
polar spaces
0 references