Torsor Neron models of hyperkahler manifolds

Abstract

Let $M$ be a compact hyperkahler manifold equipped with a Lagrangian fibration $\pi:\; M \to X$, and $M'$ the smooth locus of $\pi$. We prove that over a complement to a codimension $\geq 2$ subset in $X$, the projection $\pi:\; M' \to X$ has a natural structure of a torsor over an abelian group bundle, which can be understood as a complex analytic variant of the N\'eron model construction. This gives an independent proof of a result by Y.-J. Kim.