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Twists of intermediate Jacobian fibrations

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arxiv 2411.01953 v2 pith:IUV3K6Y4 submitted 2024-11-04 math.AG

Yajnaseni Dutta , Dominique Mattei , Evgeny Shinder This is my paper · ORCID
classification math.AG
keywords ahlerassociatedcohomologycubicfourfoldgrouphyperktwists
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We study the sections, Tate--Shafarevich twists, and the period for an OG10 hyperk\"ahler Lagrangian associated to a cubic fourfold. To do so, we introduce the analytic relative Jacobian sheaf for a Lagrangian fibration of a hyperk\"ahler variety. The Tate--Shafarevich group parameterizing twists is isomorphic to the first cohomology group of this sheaf and we compute it in terms of certain analytic Brauer groups associated to the cubic fourfold. We prove that the primitive Hodge lattice of the cubic fourfold is, up to a sign, isometric to a distinguished sublattice of the second cohomology group of the associated OG10 hyperk\"ahler manifold. Among the main tools we use are intersection complexes with integral coefficients, Decomposition Theorem, Hodge modules and Deligne cohomology.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Boundedness of some fibered K-trivial varieties

    math.AG 2025-07 conditional novelty 8.0 of 10

    Fixed-dimension Calabi-Yau varieties with abelian or primitive symplectic fibrations are birationally bounded, and Lagrangian-fibered primitive symplectic varieties have finitely many deformation classes.

  2. The Tate-Shafarevich group of a polarised K3 surface

    math.AG 2025-07 conditional novelty 6.0 of 10

    For a primitive polarization h on a K3 surface S, the Tate-Shafarevich group X(S,h) parametrizes exactly the Pic^0(C_η)-torsors admitting a good hyperkähler model.

  3. Topological Regularization

    physics.gen-ph 2025-07 reject novelty 3.0 of 10

    The paper argues that ultraviolet divergences are topological boundary artifacts and that homotopy-equivalent regularizations give identical physics, but the key proof is incomplete and internally inconsistent.

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