  Let M be a closed symplectic manifold of volume V. We say that the symplectic
packings of M by ellipsoids are unobstructed if any collection of disjoint
symplectic ellipsoids (possibly of different sizes) of total volume less than V
admits a symplectic embedding to M. We show that the symplectic packings by
ellipsoids are unobstructed for all even-dimensional tori equipped with Kahler
symplectic forms and all closed hyperkahler manifolds of maximal holonomy, or,
more generally, for closed Campana simple manifolds (that is, Kahler manifolds
that are not unions of their complex subvarieties), as well as for any closed
Kahler manifold which is a limit of Campana simple manifolds in a smooth
deformation. The proof involves the construction of a Kahler resolution of a
Kahler orbifold with isolated singularities and relies on the results of
Demailly-Paun and Miyaoka on Kahler cohomology classes.
