A uniformity criterion for vector bundles on complex projective spaces (Q1127801)

After reviewing the construction of the Dirac monopole over the two-dimensional sphere, the authors generalize this construction to any compact Riemann surface. They next perform a dimensional reduction of the Seiberg-Witten equations on \(\mathbb{R}^4\) obtaining some equations on \(\mathbb{R}^2\), which are then extended to any compact Riemann surface. This is similar to Hitchin's dimensional reduction of the self-duality equations. They finish showing that the monopoles constructed previously are solutions to the reduction Seiberg-Witten equations.