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arXiv · 2508.09819

Sections of Jacobian fibrations over lines

János Kollár·Giulia Saccà
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Abstract

Let $|H|$ be a linear system on a smooth surface $S$. We study the cohomology classes of sections of the universal Jacobian over lines in $|H|$. When $S$ is a K3 surface, the universal compactified Jacobian is a hyperk\"ahler manifold, and we do not see how to reconcile our results with some of the steps in [BKV25]. v.2: Confusing typo fixed: H^g should be H^{2g}. v3: Note added: Conjecture 7 is now corrected and solved by Pascal Autissier and Andrea Fanelli (On a conjecture by Koll\'ar and Sacc\`a, arXiv:2606.26983).

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János Kollár, Giulia Saccà. 2025-08-13. Sections of Jacobian fibrations over lines. https://arxiv.org/abs/2508.09819

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