Rank jumps for Jacobians of Hyperelliptic curves on K3 surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908936775401472 |
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| author | Corpion, Ander Arriola Salgado, Cecília |
| author_facet | Corpion, Ander Arriola Salgado, Cecília |
| contents | We study Mordell-Weil rank jumps on families of jacobians of a pencil of genus-2 curves on a K3 surface defined over a number field k. We exhibit a finite extension l/k over which the subset of fibers for which the rank jumps is infinite. Moreover, we describe further geometric conditions on the K3 surface under which the rank jumps on a non-thin set of fibers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03639 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rank jumps for Jacobians of Hyperelliptic curves on K3 surfaces Corpion, Ander Arriola Salgado, Cecília Algebraic Geometry Number Theory We study Mordell-Weil rank jumps on families of jacobians of a pencil of genus-2 curves on a K3 surface defined over a number field k. We exhibit a finite extension l/k over which the subset of fibers for which the rank jumps is infinite. Moreover, we describe further geometric conditions on the K3 surface under which the rank jumps on a non-thin set of fibers. |
| title | Rank jumps for Jacobians of Hyperelliptic curves on K3 surfaces |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2604.03639 |