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Algebraic limits of Hermitian-Yang-Mills connections on Kähler surfaces
We develop a geometric way to uniformly carry out Hörmander's $L^2$-estimates for Hermitian-Yang-Mills connections with bounded energy on Kähler surfaces. We then show the Uhlenbeck convergence of smooth HYM connections on Kähler surfaces can be realized as algebraic convergence inside an analytic f
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