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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.08959 |
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| _version_ | 1866929572417634304 |
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| author | Clingher, Adrian Malmendier, Andreas Roulleau, Xavier |
| author_facet | Clingher, Adrian Malmendier, Andreas Roulleau, Xavier |
| contents | We prove that every K3 surface with automorphism group $(\mathbb{Z}/2\mathbb{Z})^2$ admits an explicit birational model as a double sextic surface. This model is canonical for Picard number greater than 10. For Picard number greater than 9, the K3 surfaces in question possess a second birational model, in the form of a projective quartic hypersurface, generalizing the Inose quartic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08959 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On projective K3 surfaces $\mathcal{X}$ with $\mathrm{Aut}(\mathcal{X})=(\mathbb{Z}/2\mathbb{Z})^2$ Clingher, Adrian Malmendier, Andreas Roulleau, Xavier Algebraic Geometry We prove that every K3 surface with automorphism group $(\mathbb{Z}/2\mathbb{Z})^2$ admits an explicit birational model as a double sextic surface. This model is canonical for Picard number greater than 10. For Picard number greater than 9, the K3 surfaces in question possess a second birational model, in the form of a projective quartic hypersurface, generalizing the Inose quartic. |
| title | On projective K3 surfaces $\mathcal{X}$ with $\mathrm{Aut}(\mathcal{X})=(\mathbb{Z}/2\mathbb{Z})^2$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2305.08959 |