Holomorphic Lagrangian fibrations - structure and examples.

A holomorphic Lagrangian fibration naturally appears in the geometry of irreducible symplectic Kähler manifolds. After reviewing some basic definitions, we will discuss some general structure theorem on singular fibers of a  Lagrangian fibration due to Matsushita, Hwang-Oguiso, along with some examples. Based on the knowledge of singular fibers, we will discuss the  existence of a natural symplectic structure on the dual fibration of a Lagrangian  fibration.