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October, 2009 Convexity properties of generalized moment maps
Yasufumi NITTA
J. Math. Soc. Japan 61(4): 1171-1204 (October, 2009). DOI: 10.2969/jmsj/06141171


In this paper, we consider generalized moment maps for Hamiltonian actions on H -twisted generalized complex manifolds introduced by Lin and Tolman [15]. 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 [13] 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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Yasufumi NITTA. "Convexity properties of generalized moment maps." J. Math. Soc. Japan 61 (4) 1171 - 1204, October, 2009.


Published: October, 2009
First available in Project Euclid: 6 November 2009

zbMATH: 1187.37082
MathSciNet: MR2588508
Digital Object Identifier: 10.2969/jmsj/06141171

Primary: 37J15
Secondary: 14J32

Keywords: convexity properties , generalized complex structures , moment maps

Rights: Copyright © 2009 Mathematical Society of Japan


Vol.61 • No. 4 • October, 2009
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