Abstract
This is the second in a series of five papers studying special Lagrangian submanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds M with singularities X1, …, Xn locally modelled on special Lagrangian cones C1, …, Cn in \mathbb CM with isolated singularities at 0. Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL M-folds X in M with conical singularities. We define the moduli space X of deformations of X in M, and construct a natural topology on it. Then we show that X is locally homeomorphic to the zeroes of a smooth map Φ: X′ → X′ between finite-dimensional vector spaces.Here the infinitesimal deformation space X′ depends only on the topology of X, and the obstruction space X′ only on the cones C1, …, Cn at X1, …, Xn. If the cones Ci are stable then X′ is zero, and X is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M.