The Intermediate Jacobian fibration of a cubic fourfold containing a plane and fibrations in Prym varieties

Abstract

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.

arXiv commentv2: Minor corrections. Added Remark 5.14. v3: order of sections changed, results unchanged, minor corrections, published version

References in corpus (7)

• Derived categories of cubic fourfolds
• Hodge theory and derived categories of cubic fourfolds
• Base manifolds for fibrations of projective irreducible symplectic manifolds
• The K3 category of a cubic fourfold
• Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems
• Birational geometry of the intermediate Jacobian fibration of a cubic fourfold
• Singular fibres of very general Lagrangian fibrations