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 ℂdouble struck P signN, Hirzebruch surfaces, the blow up of ℂdouble struck P signN at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics