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.
From: Weite Pi [view email]
[v1]
Wed, 10 Jun 2026 09:20:55 UTC (29 KB)
[v2]
Thu, 2 Jul 2026 08:23:06 UTC (30 KB)
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