Jacobian elliptic fibrations on K3s with a non-symplectic automorphism of order 3
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914833789616128 |
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| author | Meira, Felipe Zingali |
| author_facet | Meira, Felipe Zingali |
| contents | We classify Jacobian elliptic fibrations on K3 surfaces with a non-symplectic automorphism $σ$ of order 3 according to the action of $σ$ on their fibres, building on work by Garbagnati and Salgado for non-symplectic involutions. We determine the possible reducible fibres types and give Weierstrass equations for Jacobian elliptic fibration which are preserved by $σ$. For a K3 surface $X$ with Picard number at least 12 and $σ$ acting trivially on $\NS X$, we apply the Kneser--Nishiyama method to find its Jacobian elliptic fibrations, and use our method to classify them in relation to every non-symplectic automorphism of order 3 in $\Aut X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Jacobian elliptic fibrations on K3s with a non-symplectic automorphism of order 3 Meira, Felipe Zingali Algebraic Geometry 14J27 (Primary) 14J28 (Secondary) We classify Jacobian elliptic fibrations on K3 surfaces with a non-symplectic automorphism $σ$ of order 3 according to the action of $σ$ on their fibres, building on work by Garbagnati and Salgado for non-symplectic involutions. We determine the possible reducible fibres types and give Weierstrass equations for Jacobian elliptic fibration which are preserved by $σ$. For a K3 surface $X$ with Picard number at least 12 and $σ$ acting trivially on $\NS X$, we apply the Kneser--Nishiyama method to find its Jacobian elliptic fibrations, and use our method to classify them in relation to every non-symplectic automorphism of order 3 in $\Aut X$. |
| title | Jacobian elliptic fibrations on K3s with a non-symplectic automorphism of order 3 |
| topic | Algebraic Geometry 14J27 (Primary) 14J28 (Secondary) |
| url | https://arxiv.org/abs/2403.10712 |