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Journal of Geometry

, Volume 5, Issue 2, pp 159–183 | Cite as

On the Grassmanian of lines in PG(4,q) and R(1,2) reguli

  • J. W. Freeman
Article

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.

Keywords

Projective Plane Linear Representation Baer Subplanes Line Meeting Desarguesian Projective Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser-Verlag 1974

Authors and Affiliations

  • J. W. Freeman
    • 1
  1. 1.Department of MathematicsColorado State UniversityFort CollinsUSA

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