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On the graph of a function in two variables over a finite field

Authors:	Simeon Ball Michel Lavrauw

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

Abstract:	We show that if the number of directions not determined by a pointset ${\mathcal{W}}$ of ${\mathrm{AG}}(3,q), q=p^h$ , of size q² is at least p^e q then every plane intersects ${\mathcal{W}}$ in 0 modulo p^e+1 points and apply the result to ovoids of the generalised quadrangles $T_2({\cal O})$ and $T_{2}^{*}({\cal H})$ .

Keywords:	Directions determined by a function Directions determined by a set Generalised quadrangles Ovoids
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