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Let F be any field, finite or infinite, of characteristic 2. Put \pi=PG(2,F). Let H_1,H_2 be hyperconics in \pi. In this note we study the intersectionH_1\cap H_2 . In particular we obtain canonical forms for H_1,H_2 in the cases where |H_1\cap H_2|=4,5,6. One interesting consequence is that the case |H_1\cap H_2|=6 can only occur if F contains a subfield of order 4. Related results concerning ’’pencils of hyperconics‘‘ are presented in Theorems 6 through 9. This work also leads to an extension to general fields of characteristic 2 of the well-known even intersection property for hyperovals in PG(2,4) which is pursued elsewhere ([2]). |
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