Commensurability Among Deligne-Mostow Monodromy Groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915347418841088 |
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| author | Yu, Chenglong Zheng, Zhiwei |
| author_facet | Yu, Chenglong Zheng, Zhiwei |
| contents | This paper gives the commensurability classification of Deligne--Mostow ball quotients and shows that the 104 Deligne--Mostow lattices form 38 commensurability classes. First, we find commensurability relations among Deligne--Mostow monodromy groups, which are not necessarily discrete. This generalizes previous work by Sauter and Deligne--Mostow in dimension two. In this part, we consider certain projective surfaces with two fibrations over the projective line, which induce two sets of Deligne--Mostow data. Correspondences between moduli spaces provide a geometric realization of commensurability relations. Secondly, we obtain commensurability invariants from conformal classes of Hermitian forms and toroidal boundary divisors. This completes the commensurability classification of Deligne--Mostow lattices and provides an alternative approach to the results of Kappes--M{ö}ller and McMullen on non-arithmetic Deligne--Mostow lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09682 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commensurability Among Deligne-Mostow Monodromy Groups Yu, Chenglong Zheng, Zhiwei Algebraic Geometry Group Theory Geometric Topology 14D05, 22E40 This paper gives the commensurability classification of Deligne--Mostow ball quotients and shows that the 104 Deligne--Mostow lattices form 38 commensurability classes. First, we find commensurability relations among Deligne--Mostow monodromy groups, which are not necessarily discrete. This generalizes previous work by Sauter and Deligne--Mostow in dimension two. In this part, we consider certain projective surfaces with two fibrations over the projective line, which induce two sets of Deligne--Mostow data. Correspondences between moduli spaces provide a geometric realization of commensurability relations. Secondly, we obtain commensurability invariants from conformal classes of Hermitian forms and toroidal boundary divisors. This completes the commensurability classification of Deligne--Mostow lattices and provides an alternative approach to the results of Kappes--M{ö}ller and McMullen on non-arithmetic Deligne--Mostow lattices. |
| title | Commensurability Among Deligne-Mostow Monodromy Groups |
| topic | Algebraic Geometry Group Theory Geometric Topology 14D05, 22E40 |
| url | https://arxiv.org/abs/2411.09682 |