Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds

TL;DR

This paper extends deformation theory of Lagrangian subvarieties in holomorphic symplectic manifolds to include normal crossing cases, with applications to singular fibers in Lagrangian fibrations.

Contribution

It generalizes Voisin's theorem to Lagrangian normal crossing subvarieties and provides partial results for arbitrary Lagrangian subvarieties.

Findings

Extended deformation results to normal crossing cases

Partial results for general Lagrangian subvarieties

Applied findings to study singular fibers in fibrations

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.