Finite abelian groups acting on rationally connected threefolds II: groups of K3 type
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914342741475328 |
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| author | Loginov, Konstantin Pinardin, Antoine Zhang, Zhijia |
| author_facet | Loginov, Konstantin Pinardin, Antoine Zhang, Zhijia |
| contents | We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular, if a finite abelian group faithfully acts on a threefold preserving a K3 surface (with at worst du Val singularities), then such a group is of K3 type. We prove a classification theorem for the groups of K3 type which can act on three-dimensional rationally connected varieties. We note the relation between certain groups of K3 type and K3 surfaces with higher Picard number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite abelian groups acting on rationally connected threefolds II: groups of K3 type Loginov, Konstantin Pinardin, Antoine Zhang, Zhijia Algebraic Geometry We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular, if a finite abelian group faithfully acts on a threefold preserving a K3 surface (with at worst du Val singularities), then such a group is of K3 type. We prove a classification theorem for the groups of K3 type which can act on three-dimensional rationally connected varieties. We note the relation between certain groups of K3 type and K3 surfaces with higher Picard number. |
| title | Finite abelian groups acting on rationally connected threefolds II: groups of K3 type |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.02531 |