The essential and Cremona dimensions of a group
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917451672846336 |
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| author | Dolgachev, Igor |
| author_facet | Dolgachev, Igor |
| contents | The Cremona dimension of a group $G$ is the minimal $n$ such that $G$ is isomorphic to a subgroup of the Cremona group of birational transformations of an $n$-dimensional rational variety. In this survey article, we give many examples that gives evidence to the conjecture that the Cremona dimension of a finite group over the field of complex numbers is less than or equal to the essential dimension of the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The essential and Cremona dimensions of a group Dolgachev, Igor Algebraic Geometry Group Theory 14E07, 14L30, 20G10 The Cremona dimension of a group $G$ is the minimal $n$ such that $G$ is isomorphic to a subgroup of the Cremona group of birational transformations of an $n$-dimensional rational variety. In this survey article, we give many examples that gives evidence to the conjecture that the Cremona dimension of a finite group over the field of complex numbers is less than or equal to the essential dimension of the group. |
| title | The essential and Cremona dimensions of a group |
| topic | Algebraic Geometry Group Theory 14E07, 14L30, 20G10 |
| url | https://arxiv.org/abs/2507.15096 |