Abstract
A combinatorial characterization of the Veronese variety of all quadrics in PG(n, q) by means of its intersection properties with respect to subspaces is obtained. The result relies on a similar combinatorial result on the Veronesean of all conics in the plane PG(2, q) by Ferri [Atti Accad. Naz. Lincei Rend. 61(6), 603–610 (1976)], Hirschfeld and Thas [General Galois Geometries. Oxford University Press, New York (1991)], and Thas and Van Maldeghem [European J. Combin. 25(2), 275–285 (2004)], and a structural characterization of the quadric Veronesean by Thas and Van Maldeghem [Q. J. Math. 55(1), 99–113 (2004)].
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