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The Kähler-Yang-Mills equations are coupled equations for a Kähler metric on a compact complex manifold and a connection on a complex vector bundle over it. After briefly reviewing the main aspects of the geometry of the Kähler-Yang-Mills equations, we consider dimensional reductions of the equations related to vortices — solutions to certain Yang-Mills-Higgs equations.
Oscar García‐Prada (Thu,) studied this question.