Finite groups of symplectic birational transformations of IHS manifolds of $OG10$ type
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913907547832320 |
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| author | Marquand, Lisa Muller, Stevell |
| author_facet | Marquand, Lisa Muller, Stevell |
| contents | We classify finite groups that act faithfully by symplectic birational transformations on an irreducible holomorphic symplectic (IHS) manifold of OG10 type. In particular, if X is an IHS manifold of OG10 type and G a finite subgroup of symplectic birational transformations of X, then the action of G on H2(X, Z) is conjugate to a subgroup of one of 375 groups of isometries. We prove a criterion for when such a group is determined by a group of automorphisms acting on a cubic fourfold, and apply it to our classification. Our proof is computer aided and our results are available in a Zenodo dataset. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_06580 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite groups of symplectic birational transformations of IHS manifolds of $OG10$ type Marquand, Lisa Muller, Stevell Algebraic Geometry Number Theory 14J42, 14Q15, 14E07, 14J50, 11H56 We classify finite groups that act faithfully by symplectic birational transformations on an irreducible holomorphic symplectic (IHS) manifold of OG10 type. In particular, if X is an IHS manifold of OG10 type and G a finite subgroup of symplectic birational transformations of X, then the action of G on H2(X, Z) is conjugate to a subgroup of one of 375 groups of isometries. We prove a criterion for when such a group is determined by a group of automorphisms acting on a cubic fourfold, and apply it to our classification. Our proof is computer aided and our results are available in a Zenodo dataset. |
| title | Finite groups of symplectic birational transformations of IHS manifolds of $OG10$ type |
| topic | Algebraic Geometry Number Theory 14J42, 14Q15, 14E07, 14J50, 11H56 |
| url | https://arxiv.org/abs/2310.06580 |