Deformations of symplectic vortices

TL;DR

This paper proves a gluing theorem for symplectic vortices on complex curves, demonstrating the moduli space's stratified-smooth orbifold structure and its non-canonical $C^1$-orbifold nature, advancing understanding of vortex moduli spaces.

Contribution

It establishes a gluing theorem for symplectic vortices and characterizes the moduli space as a stratified-smooth topological orbifold with a non-canonical $C^1$ structure.

Findings

Moduli space has stratified-smooth orbifold structure.

Proves a gluing theorem for symplectic vortices.

Shows the moduli space has a non-canonical $C^1$-orbifold structure.

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.