The GIT aspect of generalized K$\ddot{a}$hler reduction. I

Abstract

We revisit generalized K$\ddot{a}$hler reduction introduced by Lin and Tolman in \cite{LT} from a viewpoint of geometric invariant theory. It is shown that in the strong Hamiltonian case introduced in the present paper, many well-known conclusions of ordinary K$\ddot{a}$hler reduction can be generalized without much effort to the generalized setting. It is also shown how generalized holomorphic structures arise naturally from the reduction procedure.

arXiv comment28 pages, improved in presentation

References in corpus (7)

• Reduction of Courant algebroids and generalized complex structures
• Generalized complex geometry
• Symmetries in generalized Kähler geometry
• Generalized Kahler and hyper-Kahler quotients
• Topology of generalized complex quotients
• Convexity properties for generalized moment maps I
• Metric Reduction and Generalized Holomorphic Structures

Cited by in corpus (3)

• Toric generalized Kaehler structures. III
• Metric Reduction and Generalized Holomorphic Structures
• Toric generalized K$\ddot{a}$hler structures. I