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Ovoids of PG(3, q ), q Even, with a Conic Section
Author(s) -
Brown Matthew R.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001137
Subject(s) - conic section , ovoid , quadric , section (typography) , mathematics , plane (geometry) , isomorphism (crystallography) , geometry , combinatorics , pure mathematics , computer science , crystallography , chemistry , operating system , crystal structure
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 T 2 (C) (C 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.