De Beule, Jan

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Ghent University Academic Bibliography

Partial Spreads of T2(O)J. De Beule(joint work with M. R. Brown and L. Storme)MSC2000: 51E12, 51E23A detailed study of spreads of the generalized quadrangle T2(O) arisingfrom an oval O in PG(2, q) was made by M. R. Brown et al. in [2]. We willdiscuss partial spreads of T2(O).Assuming the partial spread of size q2 + 1 − δ is maximal and usingresults on minihypers, which are closely related to blocking sets in PG(2, q),we obtain minimal values for the deficiency δ of the maximal partial spread.In the case q even and using extendability results on arcs in PG(2, q),we can prove that a maximal partial spread of T2(O) which does not cover(∞) does not exist if δ ≤ q − 1. When O is a conic, this result improves theresult of G. Tallini for T2(O) ∼= Q(4, q) ([3]), and, furthermore, this result issharp since there exist maximal partial spreads with deficiency δ = q. Alsoexamples of maximal partial spreads of T2(O) will be given.References[1] M. R. Brown, J. De Beule and L. Storme. Maximal partial spreads ofT2(O) and T3(O). (In preparation).[2] M. R. Brown, C. M. O’Keefe, S. E. Payne, T. Penttila and G. F. Royle.Spreads of T2(O), α-flocks and ovals. Preprint.[3] G. Tallini. Blocking sets with respect to planes in PG(3, q) and maximalspreads of a nonsingular quadric in PG(4, q). In Proceedings of the FirstInternational Conference on Blocking Sets (Giessen, 1989), Mitt. Math.Sem. Giessen, number 201, pages 141–147, 1991.

Partial spreads of T2(O)

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Partial spreads of T2(O)

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Ghent University Academic Bibliography