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Ovals in Translation Hyperovals and Ovoids

โœ Scribed by Christine M. O'Keefe; Tim Penttila

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
399 KB
Volume
18
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

Let แป be an ovoid of PG(3 , q ) , q even , such that each secant plane section is an oval contained in a translation hyperoval . Then แป is shown to be either an elliptic quadric or a Tits ovoid .

๐Ÿ“œ SIMILAR VOLUMES

Ovoids and monomial ovals
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โœ David G. Glynn; Christine M. O'Keefe; Tim Penttila; Cheryl E. Praeger ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Springer ๐ŸŒ English โš– 904 KB

This paper is a contribution to the classification of ovoids. We show, under some rather technical assumptions, that if an ovoid of PG(3, q) has a pencil of monomial ovals, then it is either an elliptic quadric or a Tits ovoid. Further, we show that if an ovoid of PG(3, q) has a bundle of translatio

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In PG (3, q), q even, Cherowitzo made a detailed study of flocks of a cone with a translation oval as base; also called -flocks . To a flock of a quadratic cone in PG(3, q), q even, there always corresponds a set of q#1 ovals in PG(2, q), called an oval herd. To an -flock of a cone with an arbitrary