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Convexity properties of generalized moment maps. (English) Zbl 1187.37082

The author studies the convexity properties of generalized moment maps for Hamiltonian actions on \(H\)-twisted generalized complex manifolds introduced by Y. Lin and S. Tolman [Commun. Math. Phys. 268, No. 1, 199–222 (2006; Zbl 1120.53049)]. It is considered Hamiltonian torus actions on compact connected \(H\)-twisted generalized complex manifold and proved such convexity and connectedness for generalized moment maps. For this proof the author shows that all components of the generalized moment map are Bott-Morse functions, this fact is crucial in the proof, and it is obtained by the maximum principle for pseudoholomorphic functions on almost complex manifolds. By applying the arguments of E. Lerman, E. Meinrenken, S. Tolman and C. Woodward [Topology 37, No. 2, 245–259 (1998; Zbl 0913.58023)] the obtained results are extended to the case of Hamiltonian actions of general compact Lie groups on \(H\)-twisted generalized complex orbifolds.

MSC:

37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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References:

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