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Quadratic sets on the Klein quadric
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2022-05-06 , DOI: 10.1016/j.jcta.2022.105635
Bart De Bruyn 1
Affiliation  

Consider the Klein quadric Q+(5,q) in PG(5,q). A set of points of Q+(5,q) is called a quadratic set if it intersects each plane π of Q+(5,q) in a possibly reducible conic of π, i.e. in a singleton, a line, an irreducible conic, a pencil of two lines or the whole of π. A quadratic set is called good if at most two of these possibilities occur as π ranges over all planes of Q+(5,q). We obtain several classification results for good quadratic sets. We also provide a complete classification of all good quadratic sets of Q+(5,2) and give an explicit construction for each of them.



中文翻译:

克莱因二次曲线上的二次集

考虑克莱因二次曲线+(5,q)PG(5,q). 一组点+(5,q)如果它与每个平面π相交,则称为二次+(5,q)在一个可能可约的π二次曲线中,即在单例、一条线、一个不可约二次曲线、一条两条线的铅笔或整个π中。如果在所有平面上的π范围内最多出现两种可能性,则称二次集为+(5,q). 我们为良好的二次集获得了几个分类结果。我们还提供了所有好的二次集的完整分类+(5,2)并为它们中的每一个给出一个明确的结构。

更新日期:2022-05-06
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