Abstract
An R(1,2) regulus is a collection of q+1 mutually skew planes in PG(5,q) with the property that a line meeting three of the planes must meet all the planes. An (l,π)-configuration is the collection of lines in PG(4,q) meeting a line l and a plane π skew to l. A correspondence between (l,π)-configurations in PG(4-,q) and R(1,2) reguli in the associated Grassmanian space G(1,4) is examined. Bose has shown that R(1,2) reguli represent Baer subplanes of a Desarguesian projective plane in a linear representation of the plane. With the purpose of examining the relations between two Baer subplanes of PG(2,q2), the author examines the possible intersections of a 3-flat with an R(1,2) regulus.
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This work was supported (in part) by National Science Foundation Grant No. GP-40583.
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Freeman, J.W. On the Grassmanian of lines in PG(4,q) and R(1,2) reguli. J Geom 5, 159–183 (1974). https://doi.org/10.1007/BF01949680
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DOI: https://doi.org/10.1007/BF01949680