Annali di Matematica Pura ed Applicata

, Volume 114, Issue 1, pp 173–194 | Cite as

Partitions and their stabilizers for line complexes and quadrics

  • R. H. Dye


It is shown that PG(2Nr −1, q) can be partitioned by totally isotropic PG(r −1, q) of a non-singular line complex. The stabilizer in PSp2Nr(q) of the spread given is identified, and its geometric action is discussed. Using this partition and the various inter-relations of quadrics, line complexes and their groups when q is even we obtain various orbits of partitions of quadrics over GF(2α) by their maximal totally singular subspaces; the corresponding stabilizers in the relevant orthogonal groups are investigated. It is explained how some of these partitions naturally generalize Conwell's heptagons for the Klein quadric in PG(5, 2).


Orthogonal Group Line Complex Singular Subspace Geometric Action Klein Quadric 
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© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • R. H. Dye
    • 1
  1. 1.Newcastle upon TyneEngland

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