Singularities of the moduli space of Yang-Mills fields
The moduli space of anti self-dual instantons on a \({\mathfrak G}\)-bundle (\({\mathfrak G}\) compact, semisimple) over a Kähler surface is a complex manifold with possible singularities. This note considers the structure of the singularities which can occur. They are shown to fall into (possibly mixtures of) two types. The first occur at reducible instantons where the isotropy subgroup of the gauge group action `jumps'. Around the second type the moduli space looks like the zero point set of an analytic function. The case of a compact surface is also considered and here there are no singularities purely of the first type. Lastly for \({\mathfrak G}={\mathfrak SU}(2)\) the structure of the reducible connections is investigated.
moduli space of anti self-dual instantons
scientific article; zbMATH DE number 4023699