Contraction loci in hyperkähler manifolds

An MBM curve on a hyperkähler manifold $M$ is a rational curve with negative BBF square and minimal possible dimension of its Barlet deformation space. It is known that (up to a possible birational transform) MBM curves survive in all deformations of $M$ which leave its homology class of type $(1, 1)$. The MBM locus of an MBM curve is the union of all its deformations in the ambient manifold $M$. When $M$ is projective, this is a birational contraction locus, and all birational contraction loci are obtained this way (when $M$ is non-projective, a similar result is conjectured). I will prove that all MBM loci in a given deformation class are homeomorphic. This is a joint work with Ekaterina Amerik.