Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Deformations of holomorphic Lagrangian fibrations

Author(s): Justin Sawon
Journal: Proc. Amer. Math. Soc. 137 (2009), 279-285.
MSC (2000): Primary 53C26, 14D06, 14J60
Posted: July 10, 2008
MathSciNet review: 2439451
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Abstract: Let $X\rightarrow\mathbb{P}^n$ be a -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 . 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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