Torsor Neron models of hyperkahler manifolds

Abstract

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

10 pages, version 1.2