# Symplectic vortex equations for Kahler cones over Sasakian manifolds

## TL;DR

This paper establishes a Hitchin-Kobayashi-type correspondence for symplectic vortex equations targeting Kahler cones over Sasakian manifolds, linking solutions to geometric structures and effective divisors.

## Contribution

It introduces a novel correspondence connecting symplectic vortex equations with geometric stability conditions on Kahler cones over Sasakian manifolds.

## Key findings

- Reduced the problem to Kazdan-Warner equations
- Constructed a map between vortex moduli space and effective divisors
- Provided existence and uniqueness results for solutions

## Abstract

We obtain a Hitchin-Kobayashi-type correspondence for symplectic vortex equations, with the target a Kahler cone over a compact Sasakian manifold. We show that the correspondence reduces to studying the existence and uniqueness of Kazdan-Warner equations. Using this, we construct a map between the moduli space of solutions to the symplectic vortex equations and effective divisors.