Remarks on the Gluing Theorems for Compact Special Lagrangian Submanifolds with Isolated Conical Singularities

Abstract

Let X be a compact special Lagrangian submanifold with isolated conical singularities, and let there exist local smoothings of these singularities. It is then known that under certain hypotheses there exist global smoothings of X. We prove the same results under weaker hypotheses. We prove also that amongst these hypotheses that concerning the cohomology classes of X and the local smoothings is strictly necessary. We prove further that the global smoothings are $C^\infty$ with respect to the relevant parameters.