On <Emphasis Type="Italic">m</Emphasis>-ovoids of regular near polygons |
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| Authors: | John Bamberg " target="_blank">Jesse Lansdown " target="_blank">Melissa Lee |
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| Institution: | 1.Centre for the Mathematics of Symmetry of Computation, School of Mathematics and Statistics,University of Western Australia,Perth,Australia;2.Department of Mathematics,Imperial College,London,UK |
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| Abstract: | We generalise the work of Segre (Ann Mat Pura Appl 4(70):1–201, 1965), Cameron et al. (J Algebra 55(2):257–280, 1978), and Vanhove (J Algebr Comb 34(3):357–373, 2011) by showing that nontrivial m-ovoids of the dual polar spaces \(\mathsf {DQ}(2d, q)\), \(\mathsf {DW}(2d-1,q)\) and \(\mathsf {DH}(2d-1,q^2)\) (\(d\geqslant 3\)) are hemisystems. We also provide a more general result that holds for regular near polygons. |
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