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<p>We give a description of the intermediate Jacobian fibration attached to a general complex cubic fourfold <i>X</i> containing a plane as a Lagrangian subfibration of a moduli space of torsion sheaves on the K3 surface associated to <i>X</i> up to a cover. To do so, we propose a general construction of Lagrangian fibrations in Prym varieties as subfibrations of Beauville–Mukai systems over some loci of nodal curves in linear systems on K3 surfaces.</p>

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The intermediate jacobian fibration of a cubic fourfold containing a plane and fibrations in Prym varieties

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  • 发表日期：

    2025年1月11日

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  • Dominique Mattei

摘要

We give a description of the intermediate Jacobian fibration attached to a general complex cubic fourfold X containing a plane as a Lagrangian subfibration of a moduli space of torsion sheaves on the K3 surface associated to X up to a cover. To do so, we propose a general construction of Lagrangian fibrations in Prym varieties as subfibrations of Beauville–Mukai systems over some loci of nodal curves in linear systems on K3 surfaces.