Benoit Charbonneau, Jacques Hurtubise
Published 2008-12-01, updated 2009-10-19Version 3
In this paper, the moduli space of singular unitary Hermitian--Einstein monopoles on the product of a circle and a Riemann surface is shown to correspond to a moduli space of stable pairs on the Riemann surface. These pairs consist of a holomorphic vector bundle on the surface and a meromorphic automorphism of the bundle. The singularities of this automorphism correspond to the singularities of the singular monopole. We then consider the complex geometry of the moduli space; in particular, we compute dimensions, both from the complex geometric and the gauge theoretic point of view.
Comments: Paper revised for clarity of the arguments. We have now a cleaner and better proof of the irreducibility/stable correspondence, and of the fact that the monopole has the correct weight at the singularity. The construction of the bundle supporting the initial metric under the heat flow is much more explicit
$Z$-critical equations for holomorphic vector bundles on Kähler surfaces
Compactification of the moduli space of rho-vortices
Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
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