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Pseudo-embeddings and quadratic sets of quadrics
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2021-11-09 , DOI: 10.1007/s10623-021-00971-8
Bart De Bruyn 1 , Mou Gao 2
Affiliation  

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.



中文翻译:

伪嵌入和二次方程组

维特指数至少为 3的非奇异二次方程Q的二次集定义为与Q 的每个子空间相交的点集,该点在该子空间的可能可约的二次方程中。通过使用伪嵌入和伪超平面的理论,我们证明如果Q是二次曲面之一\(Q^+(5,2)\) , Q (6, 2), \(Q^-(7 ,2)\) ,然后的二次集Q是精确的交点Q与周围射影空间的二次曲面Q。为了实现这个目标,我们将确定Q的点和平面几何的通用伪嵌入。

更新日期:2021-11-10
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