Finding equations of the fake projective plane $(C18,p=3,\{2I\})$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915650828500992 |
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| author | Borisov, Lev Wang, Bojue |
| author_facet | Borisov, Lev Wang, Bojue |
| contents | We find explicit equations of a new pair of fake projective planes, labeled by $(C18,p=3,\{2I\})$ in the Cartwright-Steger classification. Our method involves starting with known equations of a commensurable fake projective plane $(C18,p=3,\emptyset,d_3 D_3)$ and working through a chain of cyclic covers and quotients to get to the new one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finding equations of the fake projective plane $(C18,p=3,\{2I\})$ Borisov, Lev Wang, Bojue Algebraic Geometry 14J29, 14Q10 We find explicit equations of a new pair of fake projective planes, labeled by $(C18,p=3,\{2I\})$ in the Cartwright-Steger classification. Our method involves starting with known equations of a commensurable fake projective plane $(C18,p=3,\emptyset,d_3 D_3)$ and working through a chain of cyclic covers and quotients to get to the new one. |
| title | Finding equations of the fake projective plane $(C18,p=3,\{2I\})$ |
| topic | Algebraic Geometry 14J29, 14Q10 |
| url | https://arxiv.org/abs/2512.03213 |