We study lines through the origin of finite-dimensional complex vector spaces that enjoy a doubly transitive automorphism group. In doing so, we make fundamental connections with both discrete geometry and algebraic combinatorics. In particular, we show that doubly transitive lines are necessarily optimal packings in complex projective space, and we introduce a fruitful generalization of regular abelian distance-regular antipodal covers of the complete graph.

中文翻译：

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双传递线 I：Higman 对和 roux

我们通过具有双传递自同构群的有限维复向量空间的起源来研究线。在这样做时，我们与离散几何和代数组合建立了基本联系。特别是，我们证明了双传递线必然是复杂射影空间中的最优包装，并且我们引入了完整图的正则阿贝尔距离-正则对映覆盖的富有成效的推广。