On the family of linear flocks of an absolutely irreducible hyperbolic quadric in a finite projective space
type: Item
instance of: scholarly article
title: On the family of linear flocks of an absolutely irreducible hyperbolic quadric in a finite projective space
zbMATH Open document ID: 0784.51009
author: Giorgio Faina
author: A. Bonisoli
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1992-10-01T00:00:00Z
full work available at URL: https://eudml.org/doc/244228
review text: Let \(H\) be the absolutely irreducible hyperbolic quadric in \(PG(3,q)\). A flock of \(H\) is a set of \(q+1\) disjoint circles in \(H\). The set of all intersections of \(H\) with the planes through a fixed line in \(PG(3,q)\) is an example of a flock and these flocks are called linear flocks. There are \(q^ 2(q-1)^ 2/2\) linear flocks and each pair of disjoint circles of \(H\) determines a unique linear flock. The authors prove the following theorem: If \(F\) is a set of partitions of \(H\) in circles such that each pair of disjoint circles of \(H\) is contained in exactly one member of \(F\) then \(F\) is the set of all linear flocks of \(H\).
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 52B10
zbMATH DE Number: 68879
zbMATH Keywords: quadrics
zbMATH Keywords: finite projective space
zbMATH Keywords: linear flocks
reviewed by: Dieter Betten
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 68879