Abstract
Let ϵ be a Hermitian-holomorphic vector bundle with compatible Chern connection ▽, defined on the complement o f R n inside a polydisc Δ ⊇ C n . The main result of this notes provides a necessary and sufficient condition for unique extension of ϵ to Δ, namely that the curvature F ▽, when contracted with a non-vanishing holomorphic vector field ξ, is ∂-exact. Applications to removable singularities for anti-self-dual connections across a real time line in C 2 and solutions of the static monopole equation across a point in R 3 are also given as corollaries.
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