Title: Hwang's theorem on the base of a Lagrangian fibration revisited
Abstract: Irreducible hyperkahler manifolds are higher dimensional analogs of K3 surfaces; their geometry is tightly controlled by the existence of a nowhere degenerate holomorphic 2-form. The only nontrivial fibration structure f:X -> B a hyperkahler manifold X admits is a fibration by Lagrangian tori, and for such Lagrangian fibrations the base B is conjectured to always be isomorphic to projective space. In 2008 Hwang proved that this is the case if B is assumed to be smooth by using the theory of varieties of minimal rational tangents on Fano manifolds. In this talk I will present a simpler proof of this result which leans more heavily on Hodge theory. Specifically, the main input is a basic functoriality result coming from Hodge modules. This is joint work with C. Schnell.
