Partial ovoids and partial spreads in hermitian polar spaces |
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Authors: | J De Beule A Klein K Metsch L Storme |
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Institution: | 1. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium 2. Mathematisches Institut, Justus-Liebig-Universit?t, Arndtstrasse 2, 35392, Giessen, Germany
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Abstract: | We present improved lower bounds on the sizes of small maximal partial ovoids in the classical hermitian polar spaces, and
improved upper bounds on the sizes of large maximal partial spreads in the classical hermitian polar spaces. Of particular
importance is the presented upper bound on the size of a maximal partial spread of H(3,q
2). For q = 2,3, the presented upper bound is sharp. For q = 3, our results confirm via theoretical arguments properties, deduced by computer searches performed by Ebert and Hirschfeld,
for the largest partial spreads of H(3,9). An overview of the status regarding these results is given in two summarizing tables. The similar results for the classical
symplectic and orthogonal polar spaces are presented in De Beule et al. 8].
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Keywords: | Hermitian variety Polar space Partial ovoid Partial spread |
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