We apply a modified Yang-Mills-Higgs functional to unitary bundles over closed Kahler 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 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.

Members of VBAC (Vector Bundles on Algebraic Curves), which is partially supported by EAGER (EC FP5 Contract no. HPRN-CT-2000-00099) and by EDGE (EC FP5 Contract no. HPRN-CT-2000-00101). 2 Partially supported by the National Science Foundation under grant DMS-0072073 3 Partially supported by the Ministerio de Ciencia y Tecnología (Spain) under grant BFM2000-0024 4 Partially supported by the Fundação para a Ciência e a Tecnologia (Portugal) through the Centro de Matemática da Universidade do Porto and through grant no. SFRH/BPD/1606/2000.

Suplico a vuesa merced, señor don Quijote, que mire bien y especule con cien ojos lo que hay allá dentro: quizá habrá cosas que las ponga yo en el libro de mis Transformaciones (El ingenioso hidalgo don Quijote de la Mancha, Book 2, Chapter XXII) I beg you, don Quixote sir: look carefully, inspect with a hundred eyes what you see down there. Who knows, maybe you will find something that I can put in my book on Transformations.

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