Finite abelian groups acting on rationally connected threefolds I: Groups of product type
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916546383708160 |
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| author | Loginov, Konstantin |
| author_facet | Loginov, Konstantin |
| contents | We initiate the study of finite abelian groups that faithfully act on 3-dimensional rationally connected varieties. We show that these groups can be naturally divided into three types: the groups of product type are finite abelian groups that are products of two groups which belong to the Cremona group of rank 1 and 2, respectively; the group of K3 type consists of cyclic extensions of finite abelian groups acting on a K3 surface; the third type consists of groups that act on terminal Fano threefolds with empty anti-canonical linear system. The classification of groups of product type follows from a result of J. Blanc. For the groups of K3 type, we show that there are only finitely many of them. We also formulate a conjecture regarding the groups of the third type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite abelian groups acting on rationally connected threefolds I: Groups of product type Loginov, Konstantin Algebraic Geometry We initiate the study of finite abelian groups that faithfully act on 3-dimensional rationally connected varieties. We show that these groups can be naturally divided into three types: the groups of product type are finite abelian groups that are products of two groups which belong to the Cremona group of rank 1 and 2, respectively; the group of K3 type consists of cyclic extensions of finite abelian groups acting on a K3 surface; the third type consists of groups that act on terminal Fano threefolds with empty anti-canonical linear system. The classification of groups of product type follows from a result of J. Blanc. For the groups of K3 type, we show that there are only finitely many of them. We also formulate a conjecture regarding the groups of the third type. |
| title | Finite abelian groups acting on rationally connected threefolds I: Groups of product type |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.11645 |