Summary
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).
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Entrata in Redazione il 14 giugno 1976.
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Dye, R.H. Partitions and their stabilizers for line complexes and quadrics. Annali di Matematica 114, 173–194 (1977). https://doi.org/10.1007/BF02413785
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DOI: https://doi.org/10.1007/BF02413785