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Vortices in holomorphic line bundles over closed Kähler manifolds. (English) Zbl 0717.53075
Summary: We apply a modified Yang-Mills-Higgs functional to unitary bundles over closed Kähler manifolds and study the equations which govern the global minima. The solutions represent vortices in holomorphic bundles and are direct analogs of the vortices over $${\mathbb{R}}^ 2$$. We obtain a complete description of the moduli space of these new vortices where the bundle is of rank one. The description is in terms of a class of divisors in the base manifold. There is also a dependence on a real valued parameter which can be attributed to the compactness of the base manifold.

##### MSC:
 53C80 Applications of global differential geometry to the sciences 81T13 Yang-Mills and other gauge theories in quantum field theory 53C55 Global differential geometry of Hermitian and Kählerian manifolds
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