Planar fibrations and an algebraic subvariety of the Grassmann variety (Q801528)

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 \(G_{4t,t}(F)\).