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

Let X → P 1 be an elliptically fibered K 3 surface, admitting a sequence ω i of Ricci-flat metrics collapsing the fibers. Let V be a holomorphic SU ( n ) bundle over X , stable with respect to ω i . Given the corresponding sequence Ξ i of Hermitian-Yang-Mills connections on V , we prove that, if E is a generic fiber, the restricted sequence Ξ i | E converges to a flat connection A 0 . Furthermore, if the restriction V | E is of the form ⊕ j = 1 n O E ( q j - 0 ) for n distinct points q j ∈ E , then these points uniquely determine A 0 .