OVOIDS OF PG(3,q), q EVEN, WITH A CONIC SECTION

MATTHEW R. BROWN

doi:10.1112/S0024610700001137

Abstract

It is shown that if a plane of PG(3,q), q even, meets an ovoid in a conic, then the ovoid must be an elliptic quadric. This is proved by using the generalized quadrangles T2([Cscr]) ([Cscr] a conic), W(q) and the isomorphism between them to show that every secant plane section of the ovoid must be a conic. The result then follows from a well-known theorem of Barlotti.

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OVOIDS OF PG(3,q), q EVEN, WITH A CONIC SECTION

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