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arXiv 2002.013632020-02math.AGmath.GR

有限群上的对角双小平结构

Diagonal double Kodaira structures on finite groups

Francesco Polizzi

备注：: To appear in the Proceedings of the 2019 ISAAC Congress (Aveiro, Portugal)
发表信息：: Current Trends in Analysis, its Applications and Computation, Trends in Mathematics, Birkauser, Cham (2022), 111-128
DOI：: 10.1007/978-3-030-87502-2_12

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AI总结：

本研究提出有限群的对角双Kodaira结构概念，证明其与对角双Kodaira纤维化曲面存在性等价，实现有限Heisenberg群相关结果的纯代数重述，并将其推广至任意超特殊$p$-群。

摘要：

我们引入了有限群上的一类特殊表示，称之为“对角双Kodaira（小平）结构”，其存在性等价于一类特殊Kodaira纤维化曲面（我们称为“对角双Kodaira纤维化”）的存在性。这使得我们能够用纯代数语言重新表述此前作者与A. Causin近期合作工作中得到的关于有限Heisenberg群的若干结果，并可将这些结果推广到任意超特殊$p$-群的情形。

英文摘要：

We introduce some special presentations on finite groups, that we call "diagonal double Kodaira structures" and whose existence is equivalent to the existence of some special Kodaira fibred surfaces, that we call "diagonal double Kodaira fibrations". This allows us to rephrase in purely algebraic terms some results about finite Heisenberg groups, previously obtained in the recent work of the author with A. Causin, and makes possible to extend them to the case of arbitrary extra-special $p$-groups.

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