Symmetries in generalized Kähler geometry
arXiv:math/0509069 · doi:10.1007/s00220-006-0096-z
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