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Nicholas Buchdahl, Andrei Teleman, Matei Toma, On the Donaldson–Uhlenbeck compactification of instanton moduli spaces on class VII surfaces, The Quarterly Journal of Mathematics, Volume 69, Issue 4, December 2018, Pages 1423–1473, https://doi.org/10.1093/qmath/hay026
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Abstract
We study the following question: Let be a compact Gauduchon surface, be a differentiable rank vector bundle on , be a fixed holomorphic structure on and be the Chern connection of the pair . Does the complex space structure on induced by the Kobayashi–Hitchin correspondence extend to a complex space structure on the Donaldson–Uhlenbeck compactification ? Our results answer this question in detail for the moduli spaces of -instantons with on general (possibly unknown) class VII surfaces.