Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems

L. Bader, Maska Law, G. Lunardon, Tim Penttila, N. Ourante

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)


    We construct three infinite families of partial flocks of sizes 12, 24 and 60 of the hyperbolic quadric of PG(3, q), for q congruent to -1 modulo 12, 24, 60 respectively, from the root systems of type D-4, F-4, H-4, respectively. The smallest member of each of these families is an exceptional flock. We then characterise these partial flocks in terms of the rectangle condition of Benz and by not being subflocks of linear flocks or of Thas flocks. We also give an alternative characterisation in terms of admitting a regular group fixing all the lines of one of the reguli of the hyperbolic quadric.
    Original languageEnglish
    Pages (from-to)21-30
    JournalJournal of Algebraic Combinatorics
    Publication statusPublished - 2002


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