Mathematical Research Letters
Volume 24 (2017)
Convexity for Hamiltonian torus actions on $b$-symplectic manifolds
Pages: 363 – 377
In [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 case, or they are all nonzero and the moment map behaves as in the toric $b$-symplectic case studied in [GMPS].
Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia 2016 Prize, by the Ministerio de Economía y Competitividad project with reference MTM2015-69135-P/FEDER and by the Generalitat de Catalunya project with reference 2014SGR634.
Ana Rita Pires was partially supported by a Short Visit Grant from the European Science Foundation’s “Contact and Symplectic Topology” network, and by the National Science Foundation under agreement number DMS-1128155. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Paper received on 9 December 2014.