Abstract
AbstractLet $$X\rightarrow {{\mathbb {P}}}^1$$
X
→
P
1
be an elliptically fibered K3 surface, admitting a sequence $$\omega _{i}$$
ω
i
of Ricci-flat metrics collapsing the fibers. Let V be a holomorphic SU(n) bundle over X, stable with respect to $$\omega _i$$
ω
i
. Given the corresponding sequence $$\Xi _i$$
Ξ
i
of Hermitian–Yang–Mills connections on V, we prove that, if E is a generic fiber, the restricted sequence $$\Xi _i|_{E}$$
Ξ
i
|
E
converges to a flat connection $$A_0$$
A
0
. Furthermore, if the restriction $$V|_E$$
V
|
E
is of the form $$\oplus _{j=1}^n{\mathcal {O}}_E(q_j-0)$$
⊕
j
=
1
n
O
E
(
q
j
-
0
)
for n distinct points $$q_j\in E$$
q
j
∈
E
, then these points uniquely determine $$A_0$$
A
0
.
Funder
Hellman Foundation
National Science Foundation
Simons Foundation
Publisher
Springer Science and Business Media LLC
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