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.

Keywords

irreducible symplectic manifolds, Lagrangian subvarieties, deformations

2010 Mathematics Subject Classification

13D10, 14C30, 32G10, 53D05

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Accepted 9 June 2015

Published 6 June 2016