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arXiv · 2607.27746

Families of curves separating points

Wojciech Porowski
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Abstract

We show that for a hyperbolic curve X over an algebraically closed field k of characteristic zero and a finite set S of k-rational points of X, after replacing X by a finite \'etale cover, there exists a family of curves over X whose fibres over points in S have pairwise nonisogenous Jacobians. We also give an application of our results to a problem concerning Galois sections.

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Wojciech Porowski. 2026-07-30. Families of curves separating points. https://arxiv.org/abs/2607.27746

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