Convexity properties of generalized moment maps

Details Convexity properties of generalized moment maps Convexity properties of generalized moment maps

2009-01-04

arxiv.org/abs/0901.0361v1

Mathematics

Differential Geometry

25pages, to appear in J. Math. Soc. Japan. In this paper, we extend our results in arXiv:0710.3924 to the case of Hamiltonian

Scientific paper

In this paper, we consider generalized moment maps for Hamiltonian actions on $H$-twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness properties for generalized moment maps. We study Hamiltonian torus actions on compact $H$-twisted generalized complex manifolds and prove that all components of the generalized moment map are Bott-Morse functions. Based on this, we shall show that the generalized moment maps have a convex image and connected fibers. Furthermore, by applying the arguments of Lerman, Meinrenken, Tolman, and Woodward \cite{Ler2} we extend our results to the case of Hamiltonian actions of general compact Lie groups on $H$-twisted generalized complex orbifolds.

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