On deformations of Lagrangian fibrations

Details On deformations of Lagrangian fibrations On deformations of Lagrangian fibrations

2009-03-12

arxiv.org/abs/0903.2098v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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