Symmetries in generalized Kähler geometry

Details Symmetries in generalized Kähler geometry Symmetries in generalized Kähler geometry

2005-09-04

arxiv.org/abs/math/0509069v1

Mathematics

Differential Geometry

21 pages

Scientific paper

10.1007/s00220-006-0096-z

We define the notion of a moment map and reduction in both generalized
complex geometry and generalized K\"{a}hler geometry. As an application, we
give very simple explicit constructions of bi-Hermitian structures on $\C\P^n$,
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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