Generalized Kähler metrics from Hamiltonian deformations

Abstract

We give a new characterization of generalized Kähler structures in terms of their corresponding complex Dirac structures. We then give an alternative proof of Hitchin's partial unobstructedness for holomorphic Poisson structures. Our main application is to show that there is a corresponding unobstructedness result for arbitrary generalized Kähler structures. That is, we show that any generalized Kähler structure may be deformed in such a way that one of its underlying holomorphic Poisson structures remains fixed, while the other deforms via Hitchin's deformation. Finally, we indicate a close relationship between this deformation and the notion of a Hamiltonian family of Poisson structures.

26 pages