Example of Compact Special Lagrangians with a Stable Singularity

Abstract

Abstract We construct a family of compact almost Calabi–Yau manifolds of complex dimension 3 and therein a corresponding family of compact special Lagrangians with one-point singularities modelled upon that $T^2$-cone constructed by Harvey and Lawson [7, Chapter III.3.A, Theorem 3.1] and characterised by Haskins [8, Theorem A] as a stable $T^2$-cone in the terminology by Joyce [16, Definition 3.4 and Example 3.5].