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- W2950351330 abstract "Over any field $mathbb K$, there is a bijection between regular spreads of the projective space ${rm PG}(3,{mathbb K})$ and $0$-secant lines of the Klein quadric in ${rm PG}(5,{mathbb K})$. Under this bijection, regular parallelisms of ${rm PG}(3,{mathbb K})$ correspond to hyperflock determining line sets (hfd line sets) with respect to the Klein quadric. An hfd line set is defined to be emph{pencilled} if it is composed of pencils of lines. We present a construction of pencilled hfd line sets, which is then shown to determine all such sets. Based on these results, we describe the corresponding regular parallelisms. These are also termed as being emph{pencilled}. Any Clifford parallelism is regular and pencilled. From this, we derive necessary and sufficient algebraic conditions for the existence of pencilled hfd line sets." @default.
- W2950351330 created "2019-06-27" @default.
- W2950351330 creator A5062228596 @default.
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- W2950351330 date "2017-05-20" @default.
- W2950351330 modified "2023-09-27" @default.
- W2950351330 title "Pencilled regular parallelisms" @default.
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