Abstract:
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.
