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Pseudo-embeddings and quadratic sets of quadrics

Journal Contribution - Journal Article

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.
ISSN: 1573-7586
Issue: 1
Volume: 90
Pages: 199 - 213