Obstructions to the desingularization of Special Lagrangian submanifolds

The theory of Special Lagrangian (SL) submanifolds is the natural point of intersection between various classical (Lagrangian and volume-minimizing submanifolds) and contemporary (Mirror Symmetry and invariants of Calabi-Yau manifolds) topics. The key problem is how to characterize the compactified moduli space of SLs. Equivalently, to understand which SL singularities admits desingularizations. Our aim is to present some explicit examples, topological results and simple observations which shed some light on the nature and complexity of this problem, and which we expect will be a useful foundation for future progress in the field. This is joint work with M. Haskins (Imperial College), cfr. arXiv:math/0609352.