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arXiv · 2604.03639

Rank jumps for Jacobians of Hyperelliptic curves on K3 surfaces

Ander Arriola Corpion·Cecília Salgado
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Abstract

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.

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Ander Arriola Corpion, Cecília Salgado. 2026-04-04. Rank jumps for Jacobians of Hyperelliptic curves on K3 surfaces. https://arxiv.org/abs/2604.03639

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