2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125357We study the local structure of the singularity in the moduli space of sheaves on a K3 surface which has been resolved by K O'Grady in his construction of new examples of hyperkaehler manifolds. In particular, we identify the singularity with the closure of a certain nilpotent orbit in the coadjoint representation of the group $Sp(4)$. We also prove that the moduli spaces for some other sets of numerical parameters do not admit a smooth symplectic resolution of singularities.28 pages, LaTeX2e. Final version, to appear in MMJAlgebraic Geometrytext