Deformations of Lagrangian subvarieties of holomorphic symplectic   manifolds
  We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial results are obtained for arbitrary Lagrangian subvarieties. We apply our results to the study of singular fibers of Lagrangian fibrations. 
Christian Lehn
math.AG