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We completely determine the moduli space MN,k of k vortices in $U(N)$ gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (C×CP^N-1)ᵏ/Sₖ. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. The relation to K\"ahler quotient construction is discussed.
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Eto et al. (2006) studied this question.
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