Consider the Klein quadric $Q^{+}(5,q)$ in $\mathrm{\text{PG}}(5,q)$. 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：

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克莱因二次曲线上的二次集

考虑克莱因二次曲线${问}^{+}(5,q)$在$\mathrm{\text{PG}}(5,q)$. 一组点${问}^{+}(5,q)$如果它与每个平面π相交，则称为二次集${问}^{+}(5,q)$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，则称二次集为好${问}^{+}(5,q)$. 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${问}^{+}(5,2)$并为它们中的每一个给出一个明确的结构。