Generalized Seiberg-Witten equations on a Riemann surface. (English) Zbl 1386.57031

Summary: In this paper we consider two-dimensionally reduced, generalized Seibert-Witten equations, defined on a compact Riemann surface. A novel feature of the reduction technique is that the resulting equations produce an extra “Higgs field”. Under suitable regularity assumptions, we show that the moduli space of gauge-equivalent classes of solutions to the reduced equations, is a smooth Kähler manifold and construct a pre-quantum line bundle over the moduli space of solutions.


57R57 Applications of global analysis to structures on manifolds
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53D50 Geometric quantization
35Q40 PDEs in connection with quantum mechanics
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