  We prove a Hitchin-Kobayashi correspondence for affine vortices generalizing
a result of Jaffe-Taubes for the action of the circle on the affine line.
Namely, suppose a compact Lie group K has a Hamiltonian action on a Kaehler
manifold X which is either compact or convex at infinity with a proper moment
map, and so that stable=semistable for the action of the complexified Lie group
G. Then, for some sufficiently divisible integer n, there is a bijection
between gauge equivalence classes of K-vortices with target X modulo gauge and
isomorphism classes of maps from the weighted projective line P(1,n) to X/G
that map the stacky point at infinity P(n) to the semistable locus in X. The
results allow the construction and partial computation of the quantum Kirwan
map in Woodward, and play a role in the conjectures of Dimofte, Gukov, and
Hollande relating vortex counts to knot invariants.
