Convexity for Hamiltonian torus actions on \(b\)-symplectic manifolds
This paper follows earlier work by the authors, where the Delzant theorem was generalised to \(b\)-symplectic manifolds (also known as log-symplectic). Recall that the Delzant theorem states that symplectic toric manifolds can be recovered from the image of the associated moment map. The convexity of this image is the key property on which the proof of the theorem is based. In this article the authors consider a \(b\)-symplectic manifold of dimension \(2n\), whose singular locus contains compact leaves. This manifold may be acted by a torus of dimension smaller than \(n\). Using results from [the authors et al., Int. Math. Res. Not. 2015, No. 14, 5818--5848 (2015; Zbl 1333.53115)] and following the classical proof of \textit{M. F. Atiyah} [Bull. Lond. Math. Soc. 14, 1--15 (1982; Zbl 0482.58013)], they show that the image of the moment map is convex. The modular weights associated with the exceptional hypersurface play an important role in the proof.
scientific article; zbMATH DE number 6854507