The Tate-Shafarevich group of a polarised K3 surface
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911083816550400 |
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| author | Huybrechts, Daniel Mattei, Dominique |
| author_facet | Huybrechts, Daniel Mattei, Dominique |
| contents | In an earlier paper we generalised the notion of the Tate-Shafarevich group of an elliptic K3 surface to the Tate-Shafarevich group of a polarised K3 surface. In the present note, we complement the result by proving that the Tate-Shafarevich group of a polarised K3 surface (S,h) with h primitive parametrises bijectively all torsors for the Jacobian of the generic curve in the linear system |h| that admit a good hyperkähler compactification. The result is seen as the analogue of the classical fact that the Tate-Shafarevich group of an elliptic K3 surface is the subgroup of the Weil-Châtelet group of all twists that can be compactified to a K3 surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22703 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Tate-Shafarevich group of a polarised K3 surface Huybrechts, Daniel Mattei, Dominique Algebraic Geometry 14 In an earlier paper we generalised the notion of the Tate-Shafarevich group of an elliptic K3 surface to the Tate-Shafarevich group of a polarised K3 surface. In the present note, we complement the result by proving that the Tate-Shafarevich group of a polarised K3 surface (S,h) with h primitive parametrises bijectively all torsors for the Jacobian of the generic curve in the linear system |h| that admit a good hyperkähler compactification. The result is seen as the analogue of the classical fact that the Tate-Shafarevich group of an elliptic K3 surface is the subgroup of the Weil-Châtelet group of all twists that can be compactified to a K3 surface. |
| title | The Tate-Shafarevich group of a polarised K3 surface |
| topic | Algebraic Geometry 14 |
| url | https://arxiv.org/abs/2507.22703 |