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

Nicholas Buchdahl; Andrei Teleman; Matei Toma

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

Complex Variables 2017-01-13 v1 Differential Geometry

Authors: Nicholas Buchdahl , Andrei Teleman , Matei Toma

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 ${\mathcal{M}}_a^{\mathrm{ASD}}(E)^*$ 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.

Keywords

Donaldson-Uhlenbeck compactification instanton moduli spaces class VII surfaces Gauduchon surfaces Kobayashi-Hitchin correspondence SU(2)-instantons

Cite

@article{arxiv.1701.03339,
  title  = {On the Donaldson-Uhlenbeck compactification of instanton moduli spaces on class VII surfaces},
  author = {Nicholas Buchdahl and Andrei Teleman and Matei Toma},
  journal= {arXiv preprint arXiv:1701.03339},
  year   = {2017}
}

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

Abstract

Keywords

Cite

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