Justin Sawon (Stony Brook)

"Lagrangian fibrations on holomorphic symplectic fourfolds"

Abstract: In this talk we will discuss holomorphic symplectic fourfolds
(compact hyperkahler manifolds of real dimension eight) which admit
fibrations by abelian surfaces. It is expected that every such fourfold
can be deformed to such a fibration. We will describe some recent results 
on
the polarization of the generic fibre and the degree of the discriminant
locus parametrizing singular fibres. The motivation is to classify these
Lagrangian fibrations and hence all holomorphic symplectic fourfolds.