Hermitian-Yang-Mills Connections on Collapsing Elliptically Fibered 3 Surfaces.

Let be an elliptically fibered 3 surface, admitting a sequence of Ricci-flat metrics collapsing the fibers. Let be a holomorphic () bundle over , stable with respect to . Given the corresponding sequence of Hermitian-Yang-Mills connections on , we prove that, if is a generic fiber, the restricted sequence converges to a flat connection .