Deformations of holomorphic Lagrangian fibrations

Abstract:

Let X->P^n be a 2n-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over P^n. We prove that the fibration can be deformed in a codimension one family in the moduli space Def(X) of deformations of X. If the Lagrangian fibration admits a section, we prove that there is a codimension two family of deformations which also preserve the section.

Appears in Volume 137 (2009) No. 1 of the Proceedings of the AMS. Available as math.AG/0509223 from the e-Print archive.

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