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.

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.