Manton's Vortex Equations and Anti-Self-Dual Connections

We study four of Manton's five vortex equations on a Riemann surface $X$ in relation to anti-self-dual connections. From a solution of each vortex equation, we construct an equivariant holomorphic bundle over $X$$\times$$\mathbb{P}^1$, $X$$\times$$Δ$, or $X$$\times$$\mathbb{C}$, together with an inv