On symplectic vortex equations over a compact orbifold Riemann surface

TL;DR

This paper explores symplectic vortex equations on compact orbifold Riemann surfaces using differentiable stacks, focusing on the moduli space of solutions for circle group actions on the complex plane.

Contribution

It introduces the formulation of symplectic vortex equations over orbifold Riemann surfaces and analyzes the associated moduli space of solutions.

Findings

Defined symplectic vortex equations over orbifold surfaces

Analyzed the moduli space for circle group actions

Utilized differentiable stacks to study morphisms

Abstract

Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack. After that we define symplectic vortex equations over a compact orbifold Riemann surface. We also discuss the moduli space of solutions to the equations for linear actions of the circle group on the complex plane.