Rational surfaces with a non-arithmetic automorphism group
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916432703389696 |
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| author | Li, Jennifer Torres, Sebastián |
| author_facet | Li, Jennifer Torres, Sebastián |
| contents | In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples $Y$ are Looijenga pairs, i.e., there is a connected singular nodal curve $D \subset Y$ such that $K_{Y} + D = 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08768 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational surfaces with a non-arithmetic automorphism group Li, Jennifer Torres, Sebastián Algebraic Geometry 14J50 (Primary) 14J26, 14J27 (Secondary) In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples $Y$ are Looijenga pairs, i.e., there is a connected singular nodal curve $D \subset Y$ such that $K_{Y} + D = 0$. |
| title | Rational surfaces with a non-arithmetic automorphism group |
| topic | Algebraic Geometry 14J50 (Primary) 14J26, 14J27 (Secondary) |
| url | https://arxiv.org/abs/2310.08768 |