晶格极化 K3 表面、模块形式和复反射群度的族序列

IF 1 3区数学 Q1 MATHEMATICS

Mathematische Zeitschrift Pub Date : 2024-07-30 DOI:10.1007/s00209-024-03562-0

Atsuhira Nagano

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引用次数: 0

摘要

我们介绍了一个晶格极化 K3 曲面族序列。这个序列与特殊类型的复反射群密切相关。也就是说，我们从序列所附周期映射的反对应关系中获得了模态。我们研究了模形式与复反射群不变式之间的非微妙关系。特别是，我们基于网格的算术性质和周期映射的代数几何性质，考虑了与谢泼德-托德群（Shephard-Todd group No.34）相关的一个族。

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Sequence of families of lattice polarized K3 surfaces, modular forms and degrees of complex reflection groups

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Sequence of families of lattice polarized K3 surfaces, modular forms and degrees of complex reflection groups

We introduce a sequence of families of lattice polarized K3 surfaces. This sequence is closely related to complex reflection groups of exceptional type. Namely, we obtain modular forms coming from the inverse correspondences of the period mappings attached to our sequence. We study a non-trivial relation between our modular forms and invariants of complex reflection groups. Especially, we consider a family concerned with the Shephard-Todd group No.34 based on arithmetic properties of lattices and algebro-geometric properties of the period mappings.

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