New examples of compact special lagrangian submanifolds embedded in hyper-kähler manifolds

We construct smooth families of compact special Lagrangian submanifolds embedded in some toric hyper-Kähler manifolds, which never become holomorphic Lagrangian submanifolds via any hyper-Kähler rotations. These families converge to special Lagrangian immersions with self-intersection points in the sense of currents. To construct them, we apply the desingularization method developed by Joyce.