Symmetries in generalized Kähler geometry

Abstract

We define the notion of a moment map and reduction in both generalized complex geometry and generalized Kähler geometry. As an application, we give very simple explicit constructions of bi-Hermitian structures on $\C¶^n$, Hirzebruch surfaces, the blow up of $\CP^2$ at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

21 pages

References in corpus (5)

• Reduction of Courant algebroids and generalized complex structures
• Instantons, Poisson structures and generalized Kaehler geometry
• Reduction of Generalized Complex Structures
• Hamiltonian symmetries and reduction in generalized geometry
• Generalized complex structures and Lie brackets

Cited by in corpus (39)

• Reduction of Courant algebroids and generalized complex structures
• Reduction of Generalized Complex Structures
• Generalized Kaehler Potentials from Supergravity
• Hamiltonian symmetries and reduction in generalized geometry
• Generalized Kahler geometry
• LA-Courant algebroids and their applications
• Formality in generalized Kahler geometry
• T-duality, quotients and generalized Kahler geometry
• The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction
• Twistorial construction of generalized Kaehler manifolds
• Blow-ups and resolutions of strong Kähler with torsion metrics
• Generalized geometry, equivariant $\bar{\partial }\partial$-lemma, and torus actions
• Topology of generalized complex quotients
• Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures
• Poisson structures and generalized Kahler structures
• The GIT aspect of generalized K$\ddot{a}$hler reduction. I
• Convexity properties for generalized moment maps I
• The Equivariant cohomology theory of twisted generalized complex manifolds
• Moduli spaces of Einstein-Hermitian generalized connections over generalized Kahler manifolds of symplectic type
• Non Kaehler solvmanifolds with generalized Kaehler structure
• Bihermitian metrics on Del Pezzo surfaces
• Complex Dirac structures: invariants and local structure
• Toric generalized Kaehler structures. III
• Deformations of generalized complex and generalized Kahler structures
• Metric Reduction and Generalized Holomorphic Structures
• Group actions on dg-manifolds and Exact Courant algebroids
• Reduction and construction of Poisson quasi-Nijenhuis manifolds with background
• Singular Reduction of Generalized Complex Manifolds
• Toric generalized K$\ddot{a}$hler structures. I
• Goto's generalized Kaehler stability theorem
• Bihermitian metrics on Hopf surfaces
• Metric Reduction in Generalized Geometry and Balanced Topological Field Theories
• Twist, elementary deformation, and KK correspondence in generalized complex geometry
• Chern-Weil homomorphism in twisted equivariant cohomology
• Convexity properties of generalized moment maps
• From generalized Kaehler to generalized Sasakian structures
• Flat Generalized Connections on Courant Algebroids
• Invariant generalized almost complex structures on real flag manifolds
• Generalized complex hamiltonian torus actions: Examples and constraints