Let $X\rightarrow {\mathbb P}^1$ be an elliptically fibered $K3$ surface with a section, admitting a sequence of Ricci-flat metrics collapsing the fibers. Let $\mathcal E$ be a generic, holomoprhic $SU(n)$ bundle over $X$ such that the restriction of $\mathcal E$ to each fiber is semi-stable. Given a sequence $\Xi_i$ of Hermitian-Yang-Mills connections on $\mathcal E$ corresponding to this degeneration, we prove that, if $E$ is a given fiber away from a finite set, the restricted sequence $\Xi_i|_{E}$ converges to a flat connection uniquely determined by the holomorphic structure on $\mathcal E$. 查看全文>>