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A combinatorial characterization of parabolic quadrics
No full textIn this paper we prove that, in PG(3,q), q odd, a (q^2+q+1)-set of type ((n-1)q+1,nq+1,(n+1)q+1)2, 1q/3+8/3 , such that any external line is contained in exactly one ((n-1)q+1)-secant plane is a parabolic quadric
(q^2+q+1)-caps of class [0,1,2,3,q+1]_2 and type (1,m,n)_4 of PG(5,q) are quadric Veroneseans
No full textThe quadric Veronesean V^4,2 in PG(5,q) is characterized as a (q^2+q+1)-cap of class [0,1,2,3,q+1]2 and type (1,q+1,2q+1)4 of PG(5,q) by Ferri (q odd) and Thas and Van Maldeghem (q even). In this note we generalize this result slightly by proving that for a (q^2+q+1)-cap of class [0,1,2,3,q+1]2 and type (1,m,n)4 of PG(5,q), the parameters m and n are uniquely determined and equal q+1 and 2q+1 respectively
Note on three-character (q+1)-sets in PG(3,q)
No full textWe give a combinatorial characterization of twisted cubics in PG(3, q)
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