Convexity for Hamiltonian torus actions on $b$-symplectic manifolds
Symplectic Geometry
2018-02-13 v2 Differential Geometry
Abstract
In [GMPS] we proved that the moment map image of a -symplectic toric manifold is a convex -polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on -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 -symplectic case studied in [GMPS].
Cite
@article{arxiv.1412.2488,
title = {Convexity for Hamiltonian torus actions on $b$-symplectic manifolds},
author = {Victor Guillemin and Eva Miranda and Ana Rita Pires and Geoffrey Scott},
journal= {arXiv preprint arXiv:1412.2488},
year = {2018}
}
Comments
12 pages final version to appear at Mathematical Research Letters