By Matsushita’s fundamental results, Lagrangian fibrations are essentially the only morphisms on irreducible holomorphic symplectic varieties with positive fibre dimension. We will start by reviewing these results and discuss their validity also for singular symplectic varieties. We will study singular fibres and some of the fundamental conjectures. Towards the end of the course, we will turn to some of the fascinating recent developments in the Hodge theory of Lagrangian fibrations.
These videos were produced by the Hausdorff Center for Mathematics as part of the workshop K3 surfaces, hyperkähler manifolds, and cubic fourfolds.
