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Symmetries in generalized Kähler geometry

Yi Lin·Susan Tolman
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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.

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Yi Lin, Susan Tolman. 2005-09-04. Symmetries in generalized Kähler geometry. https://doi.org/10.1007/s00220-006-0096-z

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