Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866907949648052224 |
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| author | Lonjou, Anne Przytycki, Piotr Urech, Christian |
| author_facet | Lonjou, Anne Przytycki, Piotr Urech, Christian |
| contents | We prove that any finitely generated subgroup of the plane Cremona group consisting only of algebraic elements is of bounded degree. This follows from a more general result on `decent' actions on infinite direct sums. We apply our results to describe the degree growth of finitely generated subgroups of the plane Cremona group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded Lonjou, Anne Przytycki, Piotr Urech, Christian Group Theory Algebraic Geometry Dynamical Systems 14E07, 20F65, 37F10 We prove that any finitely generated subgroup of the plane Cremona group consisting only of algebraic elements is of bounded degree. This follows from a more general result on `decent' actions on infinite direct sums. We apply our results to describe the degree growth of finitely generated subgroups of the plane Cremona group. |
| title | Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded |
| topic | Group Theory Algebraic Geometry Dynamical Systems 14E07, 20F65, 37F10 |
| url | https://arxiv.org/abs/2307.01334 |