Moduli spaces of Einstein-Hermitian generalized connections over generalized Kahler manifolds of symplectic type

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From a view point of the moment map, we shall introduce the notion of Einstein-Hermitian generalized connections over a generalized Kähler manifold of symplectic type. We show that moduli spaces of Einstein-Hermitian generalized connections arise as the Kähler quotients. The deformation complex of Einstein-Hermitian generalized connections is an elliptic complex and it turns out that the smooth part of the moduli space is a finite dimensional Kähler manifold. The canonical line bundle over a generalized Kähler manifold of symplectic type has the canonical generalized connection and its curvature coincides with "the scalar curvature as the moment map" which is defined in the previous paper [Goto₂016]. Kähler-Ricci solitons provide examples of Einstein-Hermitian generalized connections and Einstein Hermitian co-Higgs bundles are also discussed.