New examples of compact special Lagrangian submanifolds embedded in hyper-K\"ahler manifolds

TL;DR

This paper constructs new compact special Lagrangian submanifolds in hyper-Kähler manifolds that do not become holomorphic Lagrangians under any rotation, using Joyce's desingularization method.

Contribution

It introduces novel examples of special Lagrangian submanifolds in hyper-Kähler manifolds that are not holomorphic Lagrangians after any hyper-Kähler rotation.

Findings

Families converge to special Lagrangian immersions with self-intersections

New examples in toric hyper-Kähler manifolds

Application of Joyce's desingularization method

Abstract

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