Calabi-Yau varieties via cyclic covers and arithmetic ball quotients

Abstract: In this talk, we consider Calabi-Yau varieties arising from cyclic covers of smooth projective varieties branching along simple normal crossing divisors. The crepant resolutions give families of smooth Calabi-Yau manifolds. In some cases, the corresponding period maps factor through ball quotients. We give a classification of such examples for cyclic covers of some Fano varieties, especially for the product of three projective lines. This generalizes the work of Sheng-Xu-Zuo. Some of the Calabi-Yau manifolds obtained are related to the Borcea-Voisin construction and studied in Rohde’s thesis. This is joint work with Zhiwei Zheng.

Mathematics

Audience: researchers in the topic

ICCM 2020