## Journal of the Mathematical Society of Japan

### Convexity properties of generalized moment maps

Yasufumi NITTA

#### Abstract

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.

#### Article information

Source
J. Math. Soc. Japan, Volume 61, Number 4 (2009), 1171-1204.

Dates
First available in Project Euclid: 6 November 2009

https://projecteuclid.org/euclid.jmsj/1257520504

Digital Object Identifier
doi:10.2969/jmsj/06141171

Mathematical Reviews number (MathSciNet)
MR2588508

Zentralblatt MATH identifier
1187.37082

#### Citation

NITTA, Yasufumi. Convexity properties of generalized moment maps. J. Math. Soc. Japan 61 (2009), no. 4, 1171--1204. doi:10.2969/jmsj/06141171. https://projecteuclid.org/euclid.jmsj/1257520504

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