2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150257This is a second part of alg-geom/9611015. We construct a natural hyperkaehler desingularization for all singular hyperkaehler varieties. The desingularization theorem was proven in alg-geom/9611015 under additional assumption of local homogeneity. Here we show that local homogeneity is redundant: every singular hyperkaehler variety has locally homogeneous singularities.LaTeX 2e, 15 pages. This paper can be read independently from the first part. `Desingularization part I' appeared in alg-geom/9611015Algebraic Geometrytext