1,721,043 research outputs found
Two-character sets, Veronese varieties and Grassmannian of lines
No full textWe show that, for any q, the pointset covered by the conic planes of a quadric Veronesean of PG(3,q) is a two character set with respect to hyperplanes of PG(9,q)
Hyperovals arising from a Singer group action on H(3,q^2), q even
No full textFor even , a group isomorphic to
stabilizes a Baer conic inside a symplectic subquadrangle of . In this paper the action of on
points and lines of is investigated. A
construction is given of an infinite family of hyperovals of size
of , with each hyperoval having the
property that its automorphism group contains . Finally it is
shown that the hyperovals constructed are not isomorphic to known
hyperovals
Complete spans on Hermitian varieties
No full textLet L be a general linear complex in PG(3, q) for any prime power q. We show that when GF(q) is extended to GF(q(2)), the extended lines of L cover a non-singular Hermitian surface H congruent to H(3, q(2)) of PG(3, q(2)). We prove that if S is any symplectic spread PG(3, q), then the extended lines of this spread form a complete (q(2) + 1)-span of H. Several other examples of complete spans of H for small values of q are also discussed. Finally, we discuss extensions to higher dimensions, showing in particular that a similar construction produces complete (q(3) + 1)-spans of the Hermitian variety H(5, q(2))
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