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Deformations of holomorphic Lagrangian fibrations

Justin Sawon
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Abstract

Let $X\to¶^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $¶^n$. 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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Justin Sawon. 2005-09-09. Deformations of holomorphic Lagrangian fibrations. https://arxiv.org/abs/math/0509223

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