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

TL;DR

This paper describes the structure of the intermediate Jacobian fibration of a special cubic fourfold containing a plane, linking it to Prym varieties and moduli spaces on associated K3 surfaces.

Contribution

It introduces a new construction of Lagrangian fibrations in Prym varieties as subfibrations of Beauville-Mukai systems on K3 surfaces.

Findings

Describes the intermediate Jacobian fibration as a Lagrangian subfibration.

Proposes a general construction of Lagrangian fibrations in Prym varieties.

Connects the geometry of cubic fourfolds with K3 surface moduli spaces.

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.