On the Donaldson–Uhlenbeck compactification of instanton moduli spaces on class VII surfaces
Résumé
We study the following question: Let (X,g) be a compact Gauduchon surface, (E,h) be a differentiable rank r vector bundle on X, D be a fixed holomorphic structure on D≔det(E) and a be the Chern connection of the pair (D,det(h)). Does the complex space structure on MaASD(E)* induced by the Kobayashi–Hitchin correspondence extend to a complex space structure on the Donaldson–Uhlenbeck compactification M¯aASD(E)? Our results answer this question in detail for the moduli spaces of SU(2)-instantons with c2=1 on general (possibly unknown) class VII surfaces.