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On deformations of Lagrangian fibrations

Let X be an irreducible symplectic manifold and Def(X) the Kuranishi space. Assume that X admits a Lagrangian fibration. We prove that X can be deformed preserving a Lagrangian fibration. More precisely, there exists a smooth hypersurface H of Def(X) such that the restriction family over H admits a family of Lagrangian fibrations over H.

preprint2015arXivOpen access
Daisuke Matsushita
math.AGmath.DG
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Daisuke Matsushita

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