2024/01/08 by Chenglong Yu, Zhiwei Zheng, Yu, Chenglong +1
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2401.04006
In this paper we mainly study Calabi--Yau varieties that arise as triple covers of products of projective lines branched along simple normal crossing divisors. For some of those families of Calabi--Yau varieties, the period maps factor through arithmetic quotients of complex hyperbolic balls. We give a classification of such examples. One of the families was previously studied by Voisin, Borcea and Rohde. For these ball-type cases, we will show arithmeticity of the monodromy groups. These ball quotients are all commensurable to ball quotients in Deligne--Mostow theory. As a byproduct, we prove some commensurability relations among arithmetic groups in Deligne--Mostow theory.