AI 中文总结
本文分类了 Deligne-Mostow-Thurston 与十六个算术 Ghazouani-Pirio 单值群的可公度性，通过退化方法计算行列式类，证明每个后者都与某个前者可公度。
AI 中文摘要
我们分类了 Deligne--Mostow--Thurston 单值群与由球面和环面上的平坦锥度量模空间产生的十六个算术 Ghazouani--Pirio 单值群之间的可公度性关系。在这两种情形中，单值群保持一个来自扭曲同调的斜埃尔米特形式。我们使用退化方法计算亏格为一情形下的行列式类。定义 CM 域和斜埃尔米特形式的行列式类决定了可公度性关系。特别地，十六个算术 Ghazouani--Pirio 单值群中的每一个都与一个算术 Deligne--Mostow--Thurston 单值群可公度。
英文摘要
We classify commensurability relations between Deligne--Mostow--Thurston monodromy groups and the sixteen arithmetic Ghazouani--Pirio monodromy groups arising from moduli of flat cone metrics on the sphere and on the torus. In both settings, the monodromy group preserves a skew-Hermitian form coming from twisted homology. We use a degeneration method to compute their determinant classes in the genus one case. The defining CM fields and determinant classes of the skew-Hermitian forms determine the commensurability relations. In particular, each of the sixteen arithmetic Ghazouani--Pirio monodromy groups is commensurable with an arithmetic Deligne--Mostow--Thurston monodromy group.
Comments11 pages, 1 figure
