Planar fibrations and an algebraic subvariety of the Grassmann variety
type: Item
instance of: scholarly article
title: Planar fibrations and an algebraic subvariety of the Grassmann variety
zbMATH Open document ID: 0552.51003
DOI: 10.1007/BF00147873
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: Let \(S_{t,2}(F)\) a Segre variety of the projective space PG(2t-1,F) over the field F; in this work at first the author proves that a so called \(''(t-1)-regulus''\) of \(PG(2t-1,F)\) associated to \(S_{t,2}(F)\) may be represented on a Grassmann variety \(G_{2t,t}(F)\) by a normal rational curve. - Successively the ''indicator set'' associated to a planar spread of \(PG(2t-1,F)\) is constructed; in particular also an indicator set, such that the associated planar spread is Pappian, is characterized. - By means of the previous indicator set it is proved that a planar spread of Galois may be represented on the Grassmann variety \(G_{2t,t}(F)\) by an algebraic variety \(O_ t(F)\), whose properties are studied in detail, particularly when F is a Galois field. At last a class of regular switching sets contained in a planar spread of \(PG(4t-1,F)\) is represented on a Grassmann variety \(G_{4t,t}(F)\).
reviewed by: V.Dicuonzo
Mathematics Subject Classification ID: 51A30
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 51D20
zbMATH DE Number: 3879613
zbMATH Keywords: Segre variety
zbMATH Keywords: Grassmann variety
zbMATH Keywords: indicator set
zbMATH Keywords: planar spread
zbMATH Keywords: regular switching sets
author: Guglielmo Lunardon
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3879613