We study the exceptional loci of birational (bimeromorphic) contractions of a hyperkähler manifold M. Such a contraction locus is the union of all minimal rational curves in a collection of cohomology classes which are orthogonal to a wall of the Kähler cone. Cohomology classes which can possibly be orthogonal to a wall of the Kähler cone of some deformation of M are called MBM classes. We prove that all MBM classes of type (1,1) can be represented by rational curves, called MBM curves. Any MBM curve can be contracted on an appropriate birational model of M, unless \(b_2(M) \leqslant 5\). When \(b_2(M)>5\), this property can be used as an alternative definition of an MBM class and an MBM curve. Using the results of Bakker and Lehn, we prove that the stratified diffeomorphism type of a contraction locus remains stable under all deformations for which these classes remains of type (1,1), unless the contracted variety has \(b_2\leqslant 4\). Moreover, these diffeomorphisms preserve the MBM curves, and induce biholomorphic maps on the contraction fibers, if they are normal.

我们研究了 hyperkähler 流形M的双有理（双亚形）收缩的特殊位点。这种收缩轨迹是与 Kähler 锥壁正交的一组上同调类中的所有最小有理曲线的并集。可能与M的某些变形的 Kähler 锥壁正交的上同调类称为MBM 类。我们证明所有类型 (1,1) 的 MBM 类都可以用有理曲线表示，称为MBM 曲线。任何 MBM 曲线都可以在M的适当双有理模型上收缩，除非\(b_2(M) \leqslant 5\)。当\(b_2(M)>5\)，此属性可用作 MBM 类和 MBM 曲线的替代定义。使用 Bakker 和 Lehn 的结果，我们证明了收缩轨迹的分层微分同胚类型在这些类保持为 (1,1) 类型的所有变形下保持稳定，除非收缩变体具有\(b_2\leqslant 4\) . 此外，这些微分同胚保留了 MBM 曲线，并在收缩纤维上诱导双全纯图（如果它们是正常的）。