Lagrangian fibrations in six dimensions

In this talk we will consider Lagrangian fibrations of symplectic varieties in dimension six. These are fibrations by abelian threefolds over projective space P^3. We will describe Lagrangian fibrations on the known smooth symplectic varieties and Lagrangian fibrations by Prym varieties on symplectic orbifolds. Then we will see how to produce additional examples by constructing dual fibrations.