Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom