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.

v2: Minor corrections. Added Remark 5.14. v3: order of sections changed, results unchanged, minor corrections, published version

References in corpus (2)

• Base manifolds for fibrations of projective irreducible symplectic manifolds
• Birational geometry of the intermediate Jacobian fibration of a cubic fourfold