Holomorphic curves in symplectic quotients are related, via an adiabatic limit argument, to solutions of a Vortex type equation in the ambient space, which couples the curvature of a connection with the moment map. The comparison theorem gives rise, under certain hypotheses, to a surjective ring homomorphism from the equivariant cohomology of the ambient space to the quantum cohomology of the quotient. In certain cases the Vortex type equation speciales to the anti-self-duality equations, respectively the Seiberg-Witten equations, over a symplectic four-manifold.
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