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

摘要

We construct smooth families of compact special Lagrangian submanifoldsembedded in some toric hyper-K"ahler manifolds, which never becomeholomorphic Lagrangian submanifolds via any hyper-K"ahler rotations. Thesefamilies converge to special Lagrangian immersions with self-intersectionpoints in the sense of current. To construct them, we apply thedesingularization method developed by Joyce.