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Ruled cubic surfaces in PG(4,q), Baer subplanes of PG(2,q2) and Hermitian curves

2002
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Discrete Mathematics
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In PG(2; q 2 ) let '∞ denote a ÿxed line, then the Baer subplanes which intersect '∞ in q + 1 points are called a ne Baer subplanes. Call a Baer subplane of PG(2; q 2 ) non-a ne if it intersects '∞ in a unique point. It is shown by Vincenti (Boll. Un. Mat. Ital. Suppl. 2 (1980) 31) and Bose et al. (Utilitas Math. 17 (1980) 65) that non-a ne Baer subplanes of PG(2; q 2 ) are represented by certain ruled cubic surfaces in the Andrà e=Bruck and Bose representation of PG(2; q 2 ) in PG(4; q) (Math.

doi:10.1016/s0012-365x(01)00182-0
fatcat:27qjavb25rd5zaoleb77fbz4ra