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Home > Vol 23, No 3 (2006)

Simeon Ball and Michel Lavrauw

Universitat Politècnica de Catalunya Departament de Matemàtica Aplicada IV Jordi Girona 1-3, Mòdul C3, Campus Nord 08034 Barcelona Spain Jordi Girona 1-3, Mòdul C3, Campus Nord 08034 Barcelona Spain

We show that if the number of directions not determined by a pointset W {\mathcal{W}} of AG(3, q), q= p ^h {\mathrm{AG}}(3,q), q=p^h , of size q ² is at least p ^e q then every plane intersects W {\mathcal{W}} in 0 modulo p ^e+1 points and apply the result to ovoids of the generalised quadrangles T ₂( O) T_2({\cal O}) and T ₂ ^*( H) T_{2}^{*}({\cal H}) .

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