Twists of intermediate Jacobian fibrations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908390142246912 |
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| author | Dutta, Yajnaseni Mattei, Dominique Shinder, Evgeny |
| author_facet | Dutta, Yajnaseni Mattei, Dominique Shinder, Evgeny |
| contents | We study the sections, Tate--Shafarevich twists, and the period for an OG10 hyperkähler Lagrangian associated to a cubic fourfold. To do so, we introduce the analytic relative Jacobian sheaf for a Lagrangian fibration of a hyperkähler 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 hyperkähler manifold. Among the main tools we use are intersection complexes with integral coefficients, Decomposition Theorem, Hodge modules and Deligne cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twists of intermediate Jacobian fibrations Dutta, Yajnaseni Mattei, Dominique Shinder, Evgeny Algebraic Geometry We study the sections, Tate--Shafarevich twists, and the period for an OG10 hyperkähler Lagrangian associated to a cubic fourfold. To do so, we introduce the analytic relative Jacobian sheaf for a Lagrangian fibration of a hyperkähler 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 hyperkähler manifold. Among the main tools we use are intersection complexes with integral coefficients, Decomposition Theorem, Hodge modules and Deligne cohomology. |
| title | Twists of intermediate Jacobian fibrations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.01953 |