Characterizations of the finite quadric Veroneseans V-n(2n)

Wegeneralize and complete several characterizations of the finite quadric Veroneseans surveyed in Hirschfeld and Thas, General Galois Geometries , OUP, 1991. Our main result is a characterization of the quadric Veronesean V2 n in terms of the subspaces of the ambient projective space generated by the sub-Veroneseans isomorphic to V2 n−1 . Wealso obtain, as an application, acompletely new characterization of V2 n .