On the Donaldson-Uhlenbeck compactification of instanton moduli spaces on class VII surfaces

Abstract

We study the following question: Let $(X,g)$ be a compact Gauduchon surface, $(E,h)$ be a differentiable rank $r$ vector bundle on $X$, $\mathcal{D}$ be a fixed holomorphic structure on $D:=\det (E)$ and $a$ be the Chern connection of the pair $(\mathcal{D},\det (h))$. Does the complex space structure on ${\mathcal{M}}_a^{\mathrm{ASD}}(E{)}^{\ast }$ induced by the Kobayashi-Hitchin correspondence extend to a complex space structure on the Donaldson-Uhlenbeck compactification ${\overline{\mathcal{M}}}_a^{\mathrm{ASD}}(E)$? Our results answer this question in detail for the moduli spaces of $\mathrm{SU}(2)$-instantons with $c_2=1$ on general (possibly unknown) class VII surfaces.

References in corpus (1)

• Instanton moduli spaces on non-Kählerian surfaces. Holomorphic models around the reduction loci