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

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

2008-12-01

arxiv.org/abs/0812.0221v3

Mathematics

Differential Geometry

Paper revised for clarity of the arguments. We have now a cleaner and better proof of the irreducibility/stable correspondence

Scientific paper

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.

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