Partial linear spaces built on hexagons

Alice Devillers, H. Van Maldeghem

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    We define four families of geometries with as point graph the graph - or its complement - of all elliptic hyperplanes of a given parabolic quadric in any finite 6-dimensional projective space, where adjacency is given by intersecting in a tangent 4-space. One of the classes consists of semi-partial geometries constructed in J.A. Thas [SPG-reguli and semipartial geometries, Adv. Geom. 1 (2001) 229-244], for which our approach yields a new construction, more directly linked to the split Cayley hexagon. Our main results determine the complete automorphism groups of all these geometries. (c) 2005 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)901-915
    JournalEuropean Journal of Combinatorics
    Issue number3
    Publication statusPublished - 2007

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