Mathematical Research Letters

Volume 23 (2016)

Number 2

Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds

Pages: 473 – 497



Christian Lehn (Fakultät für Mathematik, Technische Universität Chemnitz, Germany)


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.


irreducible symplectic manifolds, Lagrangian subvarieties, deformations

2010 Mathematics Subject Classification

13D10, 14C30, 32G10, 53D05

Accepted 9 June 2015

Published 6 June 2016