  In this paper we study moduli spaces of sheaves on an abelian or projective
K3 surface. If $S$ is a K3, $v=2w$ is a Mukai vector on $S$, where $w$ is
primitive and $w^{2}=2$, and $H$ is a $v-$generic polarization on $S$, then the
moduli space $M_{v}$ of $H-$semistable sheaves on $S$ whose Mukai vector is $v$
admits a symplectic resolution $\widetilde{M}_{v}$. A particular case is the
$10-$dimensional O'Grady example $\widetilde{M}_{10}$ of irreducible symplectic
manifold. We show that $\widetilde{M}_{v}$ is an irreducible symplectic
manifold which is deformation equivalent to $\widetilde{M}_{10}$ and that
$H^{2}(M_{v},\mathbb{Z})$ is Hodge isometric to the sublattice $v^{\perp}$ of
the Mukai lattice of $S$. Similar results are shown when $S$ is an abelian
surface.
