Deformations of holomorphic Lagrangian fibrations

Details Deformations of holomorphic Lagrangian fibrations Deformations of holomorphic Lagrangian fibrations

2005-09-09

arxiv.org/abs/math/0509223v1

Proc. Amer. Math. Soc. 137 (2009), no. 1, 279-285

Mathematics

Algebraic Geometry

9 pages

Scientific paper

Let $X\to\P^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $\P^n$. 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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