A hyper-Kähler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold

Abstract

For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphic symplectic form making the fibration Lagrangian. In this paper, we obtain a smooth projective compactification of the intermediate Jacobian fibration giving a ten-dimensional compact hyper-Kähler manifold, which we then show to be deformation equivalent to the exceptional example of O'Grady. This proves a conjecture by Markushevich.

final version, to appear in Acta Math

References in corpus (3)

• On the symplectic eightfold associated to a Pfaffian cubic fourfold
• Complete moduli of cubic threefolds and their intermediate Jacobians
• Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties

Cited by in corpus (1)

• Hyper-Kaehler compactification of the intermediate Jacobian fibration of a cubic fourfold : the twisted case