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Intersections of Hyperconics in Projective Planes of Even Order

✍ Scribed by Aiden A. Bruen; James M. McQuillan

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 204 KB
Volume: 7
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.2000.0294

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✦ Synopsis

We show how to lift the even intersection equivalence relation from the hyperovals of PG(2, 4) to an equivalence relation amongst sets of hyperconics in "PG(2, F ). Here, F is any "nite or in"nite "eld of characteristic two that contains a sub"eld of order 4, but does not contain a sub"eld of order 8. Moreover, we are able to determine the number of points that two hyperconics in will have in common provided some projective subplane of order 4 intersects both of them in hexads.

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