Brauer groups of smooth loci in linear systems and torsors over Jacobians of plane curves

Moritz Hartlieb; Weite Pi

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arXiv · 2606.11842

Brauer groups of smooth loci in linear systems and torsors over Jacobians of plane curves

Moritz Hartlieb·Weite Pi

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Abstract

We study Brauer groups of the smooth loci in linear systems on simply connected smooth projective varieties. Under a suitable ampleness condition, we prove that the Brauer group is at most $\mathbb Z/2 \mathbb Z$. This applies when the underlying variety is the projective plane, a very general K3 surface, or a general cubic fourfold. As an application, we compute the Tate--Shafarevich group parametrizing torsors over the relative Jacobians of universal smooth plane curves. Our approach is via a study of the $2$-nodal locus in the linear system.

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BibTeX RIS

Moritz Hartlieb, Weite Pi. 2026-06-10. Brauer groups of smooth loci in linear systems and torsors over Jacobians of plane curves. https://arxiv.org/abs/2606.11842

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