Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds

Abstract

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.

arXiv comment21 pages, rewritten according to the referee's suggestions, minor errors and typos corrected, main results improved, applications added