Abstract
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.
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Acknowledgements
The second author, Mou Gao, is supported by the National Natural Science Foundation of China (Grant No. 12001083).
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Communicated by G. Korchmaros.
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De Bruyn, B., Gao, M. Pseudo-embeddings and quadratic sets of quadrics. Des. Codes Cryptogr. 90, 199–213 (2022). https://doi.org/10.1007/s10623-021-00971-8
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DOI: https://doi.org/10.1007/s10623-021-00971-8