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Title: Hermitian–Yang–Mills Connections on Collapsing Elliptically Fibered K3 Surfaces

Let$$X\rightarrow {{\mathbb {P}}}^1$$XP1be an elliptically fiberedK3 surface, admitting a sequence$$\omega _{i}$$ωiof Ricci-flat metrics collapsing the fibers. LetVbe a holomorphicSU(n) bundle overX, stable with respect to$$\omega _i$$ωi. Given the corresponding sequence$$\Xi _i$$Ξiof Hermitian–Yang–Mills connections onV, we prove that, ifEis a generic fiber, the restricted sequence$$\Xi _i|_{E}$$Ξi|Econverges to a flat connection$$A_0$$A0. Furthermore, if the restriction$$V|_E$$V|Eis of the form$$\oplus _{j=1}^n{\mathcal {O}}_E(q_j-0)$$j=1nOE(qj-0)forndistinct points$$q_j\in E$$qjE, then these points uniquely determine$$A_0$$A0.

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Author(s) / Creator(s):
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
The Journal of Geometric Analysis
Medium: X
Sponsoring Org:
National Science Foundation
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