Deformations of holomorphic Lagrangian fibrations

Sawon, Justin

doi:10.1090/S0002-9939-08-09473-2

Deformations of holomorphic Lagrangian fibrations
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Proc. Amer. Math. Soc. 137 (2009), 279-285 Request permission

Abstract:

Let $X\rightarrow \mathbb {P}^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $\mathbb {P}^n$. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space $\mathrm {Def}(X)$ of deformations of $X$. We extend his result by proving that if the Lagrangian fibration admits a section, then there is a codimension two family of deformations which also preserve the section.

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