Uniruledness of some low-dimensional ball quotients
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914701313572864 |
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| author | Maeda, Yota |
| author_facet | Maeda, Yota |
| contents | We define reflective modular forms on complex balls and use a method of Gritsenko and Hulek to show that some ball quotients of dimensions 3, 4 and 5 are uniruled. We give examples of Hermitian lattices over the rings of integers of imaginary quadratic fields $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$ for which the associated ball quotients are uniruled. Our examples include the moduli space of 8 points on $\mathbb{P}^1$. Moreover, we find that some of their Satake-Baily-Borel compactifications are rationally chain connected modulo certain cusps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_13106 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Uniruledness of some low-dimensional ball quotients Maeda, Yota Number Theory Algebraic Geometry Primary 14G35, Secondary 11G18, 11E39 We define reflective modular forms on complex balls and use a method of Gritsenko and Hulek to show that some ball quotients of dimensions 3, 4 and 5 are uniruled. We give examples of Hermitian lattices over the rings of integers of imaginary quadratic fields $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$ for which the associated ball quotients are uniruled. Our examples include the moduli space of 8 points on $\mathbb{P}^1$. Moreover, we find that some of their Satake-Baily-Borel compactifications are rationally chain connected modulo certain cusps. |
| title | Uniruledness of some low-dimensional ball quotients |
| topic | Number Theory Algebraic Geometry Primary 14G35, Secondary 11G18, 11E39 |
| url | https://arxiv.org/abs/2008.13106 |