Ovoids with a pencil of translation ovals |
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| Authors: | Christine M O'Keefe Tim Penttila |
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| Institution: | (1) Department of Pure Mathematics, The University of Adelaide, 5005 Adelaide, South Australia, Australia;(2) Department of Mathematics, University of Western Australia, 6009 Nedlands, Western Australia, Australia |
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| Abstract: | We show that if an ovoid of PG(3, q), where q>2 is even, has a pencil of translation ovals and if the carrier of the pencil is not an axis of at least one of the ovals in the pencil, then the ovoid is a Tits ovoid. It follows, as a corollary of this and a result of Penttila and Praeger, that if an ovoid of PG(3, q), where q>2 is even, has a pencil of translation ovals then the ovoid is either an elliptic quadric or a Tits ovoid. |
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| Keywords: | 51E20 |
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