Gromov-Hausdorff limits of hyperkahler metrics

Gromov defined a structure of a metric space on the set of isometry classes of metric spaces, and applied its convergence properties in areas as diverse as symplectic geometry and group theory. This metric is often called "Gromov-Hausdorff metric". I would explain what happens with Gromov-Hausdorff convergence in hyperkahler geometry.
Let $(M,I)$ be a holomorphically symplectic compact Kahler manifold, and $W$ the space of all hyperkahler metrics on all birational models of $(M,I)$. I will show that the set of Gromov-Hausdorff limits of points in $W$ contains all hyperkahler metrics on $M$. This is surprising, because the dimension of $W$ is $b_2-2$, and the dimension of its closure is at least $3b_2-8$: typically, much bigger.