Calabi-Yau Varieties via Cyclic Covers, and Complex Hyperbolic Structures for their Moduli Spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909065230155776 |
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| author | Yu, Chenglong Zheng, Zhiwei |
| author_facet | Yu, Chenglong Zheng, Zhiwei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04006 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calabi-Yau Varieties via Cyclic Covers, and Complex Hyperbolic Structures for their Moduli Spaces Yu, Chenglong Zheng, Zhiwei Algebraic Geometry 14J32, 14J10 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. |
| title | Calabi-Yau Varieties via Cyclic Covers, and Complex Hyperbolic Structures for their Moduli Spaces |
| topic | Algebraic Geometry 14J32, 14J10 |
| url | https://arxiv.org/abs/2401.04006 |