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In this paper, the moduli space of singular unitary Hermitian--Einsteinmonopoles on the product of a circle and a Riemann surface is shown tocorrespond to a moduli space of stable pairs on the Riemann surface. Thesepairs consist of a holomorphic vector bundle on the surface and a meromorphicautomorphism of the bundle. The singularities of this automorphism correspondto the singularities of the singular monopole. We then consider the complexgeometry of the moduli space; in particular, we compute dimensions, both fromthe complex geometric and the gauge theoretic point of view.

Singular Hermitian-Einstein monopoles on the product of a circle and a Riemann surface