Deformations of symplectic vortices

Abstract

We prove a gluing theorem for a symplectic vortex on a compact complex curve and a collection of holomorphic sphere bubbles. Using the theorem we show that the moduli space of regular stable symplectic vortices on a fixed curve with varying markings has the structure of a stratified-smooth topological orbifold. In addition, we show that the moduli space has a non-canonical $C^1$-orbifold structure.