A hyper-K\"ahler compactification of the Intermediate Jacobian fibration   associated to a cubic fourfold
  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-K\"ahler manifold, which we then show to be deformation equivalent to the exceptional example of O'Grady. This proves a conjecture by Markushevich. 
Radu Laza, Giulia Sacc\`a, Claire Voisin
math.AG