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

Abstract

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 [Goto_2016]. Kähler-Ricci solitons provide examples of Einstein-Hermitian generalized connections and Einstein Hermitian co-Higgs bundles are also discussed.

arXiv comment30 pages

References in corpus (9)

• Instantons, Poisson structures and generalized Kaehler geometry
• Symmetries in generalized Kähler geometry
• Constructing co-Higgs bundles on CP^2
• Compact moduli of noncommutative projective planes
• Unobstructed deformations of generalized complex structures induced by $C^{\infty }$ logarithmic symplectic structures and logarithmic Poisson structures
• Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures
• Generalized Kähler-Ricci flow and the classification of nondegenerate generalized Kähler surfaces
• Poisson structures and generalized Kahler structures
• Deformations of generalized complex and generalized Kahler structures

Cited by in corpus (2)

• Toric generalized Kaehler structures. III
• Matsushima-Lichnerowicz type theorems of Lie algebra of automorphisms of generalized Kähler manifolds of symplectic type