Generalised Seiberg-Witten equations and almost-Hermitian geometry

As an application, we show that when the hyperKähler manifold is of dimension four, then, away from a singular set, the equations can be expressed as a second order PDE in terms of almost-complex structure on the base manifold, and a conformal factor. This extends a result of Donaldson to generalised Seiberg-Witten equations.