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Original language | English |
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Publication status | E-pub ahead of print - 4 Nov 2024 |
Abstract
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- math.AG
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2024.
Research output: Working paper/Preprint › Preprint
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TY - UNPB
T1 - Twists of intermediate Jacobian fibrations
AU - Dutta, Yajnaseni
AU - Mattei, Dominique
AU - Shinder, Evgeny
N1 - Comments are welcome
PY - 2024/11/4
Y1 - 2024/11/4
N2 - 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.
AB - 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.
KW - math.AG
M3 - Preprint
BT - Twists of intermediate Jacobian fibrations
ER -