Convexity for Hamiltonian torus actions on b-symplectic manifolds
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n [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic manifolds. The modular weights of the action on the connected components of the exceptional hypersurface play a fundamental role: either they are all zero and the moment map behaves as in classic symplectic one, or they are all nonzero and the moment map behaves as in the toric b-symplectic case studied in [GMPS].
CitationGuillemin, V. [et al.]. Convexity for Hamiltonian torus actions on b-symplectic manifolds. "Mathematical research letters", 2017, vol. 24, núm. 2, p. 363-377.