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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.00607 |
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| _version_ | 1866914947441623040 |
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| author | Golota, Aleksei |
| author_facet | Golota, Aleksei |
| contents | Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not exceed $2\dim(X)$. Moreover, the equality holds if and only if $X$ is birational to an abelian variety. We also show that an analogous result holds for groups of bimeromorphic automorphisms of compact Kähler spaces, under some additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_00607 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps Golota, Aleksei Algebraic Geometry Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not exceed $2\dim(X)$. Moreover, the equality holds if and only if $X$ is birational to an abelian variety. We also show that an analogous result holds for groups of bimeromorphic automorphisms of compact Kähler spaces, under some additional assumptions. |
| title | Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2205.00607 |