Pseudo-embeddings and quadratic sets of quadrics.

A quadratic set of a nonsingular quadric Q of Witt index at least three is defined as a set of points intersecting each subspace of Q in a possibly reducible quadric of that subspace. By using the theory of pseudo-embeddings and pseudo-hyperplanes, we show that if Q is one of the quadrics Q + (5 , 2) , Q(6, 2), Q - (7 , 2) , then the quadratic sets of Q are precisely the intersections of Q with the quadrics of the ambient projective space of Q. In order to achieve this goal, we will determine the universal pseudo-embedding of the geometry of the points and planes of Q. [ABSTRACT FROM AUTHOR]