(This is a part of Seminars on Algebraic Surfaces and Related Topics.)
The cotangent bundle of a complex projective manifold carries a natural holomorphic symplectic 2-form. The existence of a natural Lagrangian fibration structure of these non-compact complex manifolds has not been studied very much. In this talk, I will present a natural Lagrangian fibration structure on the map from the cotangent bundle of a del Pezzo surface of degree 4. This is a joint work with Prof. Yongnam Lee.