Example of Compact Special Lagrangians with a Stable Singularity

TL;DR

This paper constructs a family of compact special Lagrangian submanifolds with stable singularities within almost Calabi--Yau manifolds, advancing understanding of singularity models in complex geometry.

Contribution

It introduces a new family of compact special Lagrangians with stable singularities modeled on a specific T^2-cone, expanding the class of known singular Lagrangian examples.

Findings

Construction of a family of compact almost Calabi--Yau manifolds.

Existence of special Lagrangians with one-point singularities.

Modeling of singularities on a Harvey--Lawson T^2-cone.

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--Lawson and characterized by Haskins as a stable T^2-cone in the terminology by Joyce.