Twists of intermediate Jacobian fibrations

Research output: Working paper/PreprintPreprint

Authors

  • Yajnaseni Dutta
  • Dominique Mattei
  • Evgeny Shinder

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Details

Original languageEnglish
Publication statusE-pub ahead of print - 4 Nov 2024

Abstract

We introduce and study the analytic relative Jacobian sheaf for a Lagrangian fibration of a hyperk\"ahler manifold. When the fibration has irreducible fibers in codimension 1 and a relative principal polarization, we show that it is isomorphic to the relative Albanese sheaf which acts on the Lagrangian fibration. We apply this to OG10 Lagrangian fibrations associated to a smooth cubic fourfold constructed by Laza-Sacc\`a-Voisin and Sacc\`a. For sufficiently general cubic fourfolds, we compute the Tate-Shafarevich group parametrizing twists of the original Lagrangian fibration in terms of certain degree twists and Brauer twists. Among the main tools we use are perverse sheaves, decomposition theorem, Hodge modules and Deligne cohomology.

Keywords

    math.AG

Cite this

Twists of intermediate Jacobian fibrations. / Dutta, Yajnaseni; Mattei, Dominique; Shinder, Evgeny.
2024.

Research output: Working paper/PreprintPreprint

Dutta, Y, Mattei, D & Shinder, E 2024 'Twists of intermediate Jacobian fibrations'.
Dutta, Y., Mattei, D., & Shinder, E. (2024). Twists of intermediate Jacobian fibrations. Advance online publication.
Dutta Y, Mattei D, Shinder E. Twists of intermediate Jacobian fibrations. 2024 Nov 4. Epub 2024 Nov 4.
Dutta, Yajnaseni ; Mattei, Dominique ; Shinder, Evgeny. / Twists of intermediate Jacobian fibrations. 2024.
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