Abstract: Irreducible holomorphic symplectic manifolds are one of the basic building blocks of manifolds with trivial canonical bundles. Surprising, the only fibrations they can admit are Lagrangian fibrations, with fibres that are Lagrangian with respect to the holomorphic symplectic structure. Ultimately, we would like to use Lagrangian fibrations to classify all holomorphic symplectic manifolds. In this talk I will describe why, after imposing some natural hypotheses, there are only finitely many deformation classes of Lagrangian fibrations. The talk will be based on the preprint arXiv:1212.6470.
