Sections of Jacobian fibrations over lines
J\'anos Koll\'ar, Giulia Sacc\`a

TL;DR
This paper investigates the cohomology classes of sections of the universal Jacobian over lines in a linear system on smooth surfaces, with a focus on K3 surfaces where the universal compactified Jacobian forms a hyperk"ahler manifold.
Contribution
It provides new insights into the cohomology classes of sections of the universal Jacobian over lines, especially in the context of K3 surfaces and hyperk"ahler geometry.
Findings
Cohomology classes of sections are characterized in specific geometric contexts.
The universal compactified Jacobian on K3 surfaces is a hyperk"ahler manifold.
Identifies discrepancies with previous results in [BKV25].
Abstract
Let be a linear system on a smooth surface . We study the cohomology classes of sections of the universal Jacobian over lines in . When 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}.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
