Local model for the moduli space of affine vortices

We show that the moduli space of regular affine vortices, which are solutions of the symplectic vortex equation over the complex plane, has the structure of a smooth manifold. The construction uses Ziltener’s Fredholm theory results [31]. We also extend the result to the case of affine vortices over the upper half plane. These results are necessary ingredients in defining the “open quantum Kirwan map” proposed by Woodward [24].