# Generalised monopole equations on Kahler surfaces

## TL;DR

This paper establishes a correspondence for generalized Seiberg-Witten monopole equations on Kahler surfaces, linking stability conditions to solution existence and mapping moduli spaces to effective divisors.

## Contribution

It extends the Hitchin-Kobayashi correspondence to generalized monopole equations on Kahler surfaces, connecting stability criteria with solution existence.

## Key findings

- Stability criterion for solutions matches that of classical Seiberg-Witten equations.
- Constructs a map from the moduli space to effective divisors.
- Provides a geometric interpretation of solutions via divisors.

## Abstract

In this article, we establish a Hitchin-Kobayashi type correspondence for generalised Seiberg-Witten monopole equations on Kahler surfaces. We show that the "stability" criterion we obtain, for the existence of solutions, coincides with that of the usual Seiberg-Witten monopole equations. This enables us to construct a map from the moduli space of solutions to the generalised equations to effective divisors.